diff --git a/changelogs/unreleased/sh-fix-branches-api-timeout.yml b/changelogs/unreleased/sh-fix-branches-api-timeout.yml
new file mode 100644
index 00000000000..8cd29a7269d
--- /dev/null
+++ b/changelogs/unreleased/sh-fix-branches-api-timeout.yml
@@ -0,0 +1,5 @@
+---
+title: Fix timeout issues retrieving branches via API
+merge_request: 24034
+author:
+type: performance
diff --git a/lib/api/branches.rb b/lib/api/branches.rb
index e7e58ad0e66..07f529b01bb 100644
--- a/lib/api/branches.rb
+++ b/lib/api/branches.rb
@@ -34,11 +34,11 @@ module API
         repository = user_project.repository
 
         branches = BranchesFinder.new(repository, declared_params(include_missing: false)).execute
-
+        branches = ::Kaminari.paginate_array(branches)
         merged_branch_names = repository.merged_branch_names(branches.map(&:name))
 
         present(
-          paginate(::Kaminari.paginate_array(branches)),
+          paginate(branches),
           with: Entities::Branch,
           current_user: current_user,
           project: user_project,
diff --git a/spec/requests/api/branches_spec.rb b/spec/requests/api/branches_spec.rb
index 93c411476bb..b38cd66986f 100644
--- a/spec/requests/api/branches_spec.rb
+++ b/spec/requests/api/branches_spec.rb
@@ -20,6 +20,12 @@ describe API::Branches do
     let(:route) { "/projects/#{project_id}/repository/branches" }
 
     shared_examples_for 'repository branches' do
+      RSpec::Matchers.define :has_merged_branch_names_count do |expected|
+        match do |actual|
+          actual[:merged_branch_names].count == expected
+        end
+      end
+
       it 'returns the repository branches' do
         get api(route, current_user), params: { per_page: 100 }
 
@@ -30,6 +36,12 @@ describe API::Branches do
         expect(branch_names).to match_array(project.repository.branch_names)
       end
 
+      it 'determines only a limited number of merged branch names' do
+        expect(API::Entities::Branch).to receive(:represent).with(anything, has_merged_branch_names_count(2))
+
+        get api(route, current_user), params: { per_page: 2 }
+      end
+
       context 'when repository is disabled' do
         include_context 'disabled repository'