diff --git a/pkg/ccl/partitionccl/BUILD.bazel b/pkg/ccl/partitionccl/BUILD.bazel
index c6c067f86f84..0c324ea21b55 100644
--- a/pkg/ccl/partitionccl/BUILD.bazel
+++ b/pkg/ccl/partitionccl/BUILD.bazel
@@ -77,6 +77,7 @@ go_test(
         "//pkg/sql/types",
         "//pkg/testutils",
         "//pkg/testutils/serverutils",
+        "//pkg/testutils/skip",
         "//pkg/testutils/sqlutils",
         "//pkg/testutils/testcluster",
         "//pkg/util/encoding",
diff --git a/pkg/ccl/partitionccl/alter_primary_key_test.go b/pkg/ccl/partitionccl/alter_primary_key_test.go
index a66838f1e035..86a55701d892 100644
--- a/pkg/ccl/partitionccl/alter_primary_key_test.go
+++ b/pkg/ccl/partitionccl/alter_primary_key_test.go
@@ -9,6 +9,7 @@ import (
 	"testing"
 
 	"github.com/cockroachdb/cockroach/pkg/ccl/testutilsccl"
+	"github.com/cockroachdb/cockroach/pkg/testutils/skip"
 	"github.com/cockroachdb/cockroach/pkg/util/leaktest"
 	"github.com/cockroachdb/cockroach/pkg/util/log"
 )
@@ -17,6 +18,9 @@ func TestAlterPrimaryKeyCorrectZoneConfigBeforeBackfill(t *testing.T) {
 	defer leaktest.AfterTest(t)()
 	defer log.Scope(t).Close(t)
 
+	skip.UnderDeadlock(t)
+	skip.UnderRace(t)
+
 	testCases := []testutilsccl.AlterPrimaryKeyCorrectZoneConfigTestCase{
 		{
 			Desc: "ALTER PRIMARY KEY",