diff --git a/pkg/ccl/kvccl/kvfollowerreadsccl/boundedstaleness_test.go b/pkg/ccl/kvccl/kvfollowerreadsccl/boundedstaleness_test.go
index 78d89de8d93c..00e6b6bfc5d3 100644
--- a/pkg/ccl/kvccl/kvfollowerreadsccl/boundedstaleness_test.go
+++ b/pkg/ccl/kvccl/kvfollowerreadsccl/boundedstaleness_test.go
@@ -263,6 +263,7 @@ func TestBoundedStalenessDataDriven(t *testing.T) {
 	defer log.Scope(t).Close(t)
 
 	skip.UnderStress(t, "1μs staleness reads may actually succeed due to the slow environment")
+	skip.UnderRace(t, "probable OOM")
 	defer ccl.TestingEnableEnterprise()()
 
 	ctx := context.Background()
diff --git a/pkg/server/application_api/schema_inspection_test.go b/pkg/server/application_api/schema_inspection_test.go
index 3158517c9eb4..54729c86f4d6 100644
--- a/pkg/server/application_api/schema_inspection_test.go
+++ b/pkg/server/application_api/schema_inspection_test.go
@@ -424,6 +424,8 @@ func TestAdminAPIDatabaseDetails(t *testing.T) {
 	defer leaktest.AfterTest(t)()
 	defer log.Scope(t).Close(t)
 
+	skip.UnderRace(t, "probable OOM")
+
 	const numServers = 3
 	tc := testcluster.StartTestCluster(t, numServers, base.TestClusterArgs{})
 	defer tc.Stopper().Stop(context.Background())
diff --git a/pkg/server/application_api/stats_test.go b/pkg/server/application_api/stats_test.go
index cc4597593f4c..a392008da9b1 100644
--- a/pkg/server/application_api/stats_test.go
+++ b/pkg/server/application_api/stats_test.go
@@ -327,6 +327,8 @@ func TestClusterResetSQLStats(t *testing.T) {
 	defer leaktest.AfterTest(t)()
 	defer log.Scope(t).Close(t)
 
+	skip.UnderRace(t, "probable OOM")
+
 	ctx := context.Background()
 
 	for _, flushed := range []bool{false, true} {
diff --git a/pkg/sql/importer/import_stmt_test.go b/pkg/sql/importer/import_stmt_test.go
index dc5c0fa095d1..25b12e98c1c6 100644
--- a/pkg/sql/importer/import_stmt_test.go
+++ b/pkg/sql/importer/import_stmt_test.go
@@ -5552,6 +5552,9 @@ func TestImportMysql(t *testing.T) {
 func TestImportIntoMysql(t *testing.T) {
 	defer leaktest.AfterTest(t)()
 	defer log.Scope(t).Close(t)
+
+	skip.UnderRace(t, "probable OOM")
+
 	const (
 		nodes = 3
 	)