diff --git a/app/graphql/mutations/groups/update.rb b/app/graphql/mutations/groups/update.rb
new file mode 100644
index 0000000000000000000000000000000000000000..f4eb94f9f8422a3999a8c191eb2484d9a1af376b
--- /dev/null
+++ b/app/graphql/mutations/groups/update.rb
@@ -0,0 +1,40 @@
+# frozen_string_literal: true
+
+module Mutations
+  module Groups
+    class Update < Mutations::BaseMutation
+      include Mutations::ResolvesGroup
+
+      graphql_name 'GroupUpdate'
+
+      authorize :admin_group
+
+      field :group, Types::GroupType,
+            null: true,
+            description: 'The group after update.'
+
+      argument :full_path, GraphQL::Types::ID,
+               required: true,
+               description: 'Full path of the group that will be updated.'
+      argument :shared_runners_setting, Types::Namespace::SharedRunnersSettingEnum,
+               required: true,
+               description: copy_field_description(Types::GroupType, :shared_runners_setting)
+
+      def resolve(full_path:, **args)
+        group = authorized_find!(full_path: full_path)
+
+        unless ::Groups::UpdateService.new(group, current_user, args).execute
+          return { group: nil, errors: group.errors.full_messages }
+        end
+
+        { group: group, errors: [] }
+      end
+
+      private
+
+      def find_object(full_path:)
+        resolve_group(full_path: full_path)
+      end
+    end
+  end
+end
diff --git a/app/graphql/types/mutation_type.rb b/app/graphql/types/mutation_type.rb
index 812943e0a1e1d65a1ca14429b266a3314ba9684a..530298ba07a33747e663fb2e584bdbe08c712b56 100644
--- a/app/graphql/types/mutation_type.rb
+++ b/app/graphql/types/mutation_type.rb
@@ -105,6 +105,7 @@ class MutationType < BaseObject
     mount_mutation Mutations::Ci::Runner::Delete, feature_flag: :runner_graphql_query
     mount_mutation Mutations::Ci::RunnersRegistrationToken::Reset, feature_flag: :runner_graphql_query
     mount_mutation Mutations::Namespace::PackageSettings::Update
+    mount_mutation Mutations::Groups::Update
     mount_mutation Mutations::UserCallouts::Create
     mount_mutation Mutations::Packages::Destroy
     mount_mutation Mutations::Packages::DestroyFile
diff --git a/doc/api/graphql/reference/index.md b/doc/api/graphql/reference/index.md
index 99b1b023524c25208cbdacaad39ebf78bab46921..b6b266ada81068e4bf07a84200b54d69e1a08465 100644
--- a/doc/api/graphql/reference/index.md
+++ b/doc/api/graphql/reference/index.md
@@ -2360,6 +2360,26 @@ Input type: `GitlabSubscriptionActivateInput`
 | <a id="mutationgitlabsubscriptionactivateerrors"></a>`errors` | [`[String!]!`](#string) | Errors encountered during execution of the mutation. |
 | <a id="mutationgitlabsubscriptionactivatelicense"></a>`license` | [`CurrentLicense`](#currentlicense) | The current license. |
 
+### `Mutation.groupUpdate`
+
+Input type: `GroupUpdateInput`
+
+#### Arguments
+
+| Name | Type | Description |
+| ---- | ---- | ----------- |
+| <a id="mutationgroupupdateclientmutationid"></a>`clientMutationId` | [`String`](#string) | A unique identifier for the client performing the mutation. |
+| <a id="mutationgroupupdatefullpath"></a>`fullPath` | [`ID!`](#id) | Full path of the group that will be updated. |
+| <a id="mutationgroupupdatesharedrunnerssetting"></a>`sharedRunnersSetting` | [`SharedRunnersSetting!`](#sharedrunnerssetting) | Shared runners availability for the namespace and its descendants. |
+
+#### Fields
+
+| Name | Type | Description |
+| ---- | ---- | ----------- |
+| <a id="mutationgroupupdateclientmutationid"></a>`clientMutationId` | [`String`](#string) | A unique identifier for the client performing the mutation. |
+| <a id="mutationgroupupdateerrors"></a>`errors` | [`[String!]!`](#string) | Errors encountered during execution of the mutation. |
+| <a id="mutationgroupupdategroup"></a>`group` | [`Group`](#group) | The group after update. |
+
 ### `Mutation.httpIntegrationCreate`
 
 Input type: `HttpIntegrationCreateInput`
diff --git a/spec/graphql/mutations/groups/update_spec.rb b/spec/graphql/mutations/groups/update_spec.rb
new file mode 100644
index 0000000000000000000000000000000000000000..2118134e8e6c83e55c1518babd21dd25e0ae0c62
--- /dev/null
+++ b/spec/graphql/mutations/groups/update_spec.rb
@@ -0,0 +1,74 @@
+# frozen_string_literal: true
+
+require 'spec_helper'
+
+RSpec.describe Mutations::Groups::Update do
+  using RSpec::Parameterized::TableSyntax
+
+  let_it_be_with_reload(:group) { create(:group) }
+  let_it_be(:user) { create(:user) }
+
+  let(:params) { { full_path: group.full_path } }
+
+  specify { expect(described_class).to require_graphql_authorizations(:admin_group) }
+
+  describe '#resolve' do
+    subject { described_class.new(object: group, context: { current_user: user }, field: nil).resolve(**params) }
+
+    RSpec.shared_examples 'updating the group shared runners setting' do
+      it 'updates the group shared runners setting' do
+        expect { subject }
+          .to change { group.reload.shared_runners_setting }.from('enabled').to('disabled_and_unoverridable')
+      end
+
+      it 'returns no errors' do
+        expect(subject).to eq(errors: [], group: group)
+      end
+
+      context 'with invalid params' do
+        let_it_be(:params) { { full_path: group.full_path, shared_runners_setting: 'inexistent_setting' } }
+
+        it 'doesn\'t update the shared_runners_setting' do
+          expect { subject }
+            .not_to change { group.reload.shared_runners_setting }
+        end
+
+        it 'returns an error' do
+          expect(subject).to eq(
+            group: nil,
+            errors: ["Update shared runners state must be one of: #{::Namespace::SHARED_RUNNERS_SETTINGS.join(', ')}"]
+          )
+        end
+      end
+    end
+
+    RSpec.shared_examples 'denying access to group shared runners setting' do
+      it 'raises Gitlab::Graphql::Errors::ResourceNotAvailable' do
+        expect { subject }.to raise_error(Gitlab::Graphql::Errors::ResourceNotAvailable)
+      end
+    end
+
+    context 'changing shared runners setting' do
+      let_it_be(:params) do
+        { full_path: group.full_path,
+          shared_runners_setting: 'disabled_and_unoverridable' }
+      end
+
+      where(:user_role, :shared_examples_name) do
+        :owner      | 'updating the group shared runners setting'
+        :developer  | 'denying access to group shared runners setting'
+        :reporter   | 'denying access to group shared runners setting'
+        :guest      | 'denying access to group shared runners setting'
+        :anonymous  | 'denying access to group shared runners setting'
+      end
+
+      with_them do
+        before do
+          group.send("add_#{user_role}", user) unless user_role == :anonymous
+        end
+
+        it_behaves_like params[:shared_examples_name]
+      end
+    end
+  end
+end
diff --git a/spec/requests/api/graphql/mutations/groups/update_spec.rb b/spec/requests/api/graphql/mutations/groups/update_spec.rb
new file mode 100644
index 0000000000000000000000000000000000000000..b9dfb8e37ab1e3c267183490c152718677c36f3f
--- /dev/null
+++ b/spec/requests/api/graphql/mutations/groups/update_spec.rb
@@ -0,0 +1,66 @@
+# frozen_string_literal: true
+
+require 'spec_helper'
+
+RSpec.describe 'GroupUpdate' do
+  include GraphqlHelpers
+
+  let_it_be(:user) { create(:user) }
+  let_it_be_with_reload(:group) { create(:group) }
+
+  let(:variables) do
+    {
+      full_path: group.full_path,
+      shared_runners_setting: 'DISABLED_WITH_OVERRIDE'
+    }
+  end
+
+  let(:mutation) { graphql_mutation(:group_update, variables) }
+
+  context 'when unauthorized' do
+    shared_examples 'unauthorized' do
+      it 'returns an error' do
+        post_graphql_mutation(mutation, current_user: user)
+
+        expect(graphql_errors).not_to be_empty
+      end
+    end
+
+    context 'when not a group member' do
+      it_behaves_like 'unauthorized'
+    end
+
+    context 'when a non-admin group member' do
+      before do
+        group.add_developer(user)
+      end
+
+      it_behaves_like 'unauthorized'
+    end
+  end
+
+  context 'when authorized' do
+    before do
+      group.add_owner(user)
+    end
+
+    it 'updates shared runners settings' do
+      post_graphql_mutation(mutation, current_user: user)
+
+      expect(response).to have_gitlab_http_status(:success)
+      expect(graphql_errors).to be_nil
+      expect(group.reload.shared_runners_setting).to eq(variables[:shared_runners_setting].downcase)
+    end
+
+    context 'when bad arguments are provided' do
+      let(:variables) { { full_path: '', shared_runners_setting: 'INVALID' } }
+
+      it 'returns the errors' do
+        post_graphql_mutation(mutation, current_user: user)
+
+        expect(graphql_errors).not_to be_empty
+        expect(group.reload.shared_runners_setting).to eq('enabled')
+      end
+    end
+  end
+end