diff --git a/modules/git/git_test.go b/modules/git/git_test.go
index 1f9060247f..01200dba68 100644
--- a/modules/git/git_test.go
+++ b/modules/git/git_test.go
@@ -105,6 +105,10 @@ func TestSyncConfigGPGFormat(t *testing.T) {
 	})
 
 	t.Run("SSH format", func(t *testing.T) {
+		if CheckGitVersionAtLeast("2.34.0") != nil {
+			t.SkipNow()
+		}
+
 		r, err := os.OpenRoot(t.TempDir())
 		require.NoError(t, err)
 		f, err := r.OpenFile("ssh-keygen", os.O_CREATE|os.O_TRUNC, 0o700)
diff --git a/tests/integration/git_push_test.go b/tests/integration/git_push_test.go
index bd7a464354..22dd127a4c 100644
--- a/tests/integration/git_push_test.go
+++ b/tests/integration/git_push_test.go
@@ -27,6 +27,10 @@ import (
 
 func forEachObjectFormat(t *testing.T, f func(t *testing.T, objectFormat git.ObjectFormat)) {
 	for _, objectFormat := range []git.ObjectFormat{git.Sha256ObjectFormat, git.Sha1ObjectFormat} {
+		if !git.SupportHashSha256 && objectFormat == git.Sha256ObjectFormat {
+			continue
+		}
+
 		t.Run(objectFormat.Name(), func(t *testing.T) {
 			f(t, objectFormat)
 		})