diff --git a/src/backend/catalog/index.c b/src/backend/catalog/index.c
index 4debe6ee87..3a24c32d14 100644
--- a/src/backend/catalog/index.c
+++ b/src/backend/catalog/index.c
@@ -218,12 +218,12 @@ index_check_primary_key(Relation heapRel,
 	int			i;
 
 	/*
-	 * If ALTER TABLE, check that there isn't already a PRIMARY KEY. In CREATE
-	 * TABLE, we have faith that the parser rejected multiple pkey clauses;
-	 * and CREATE INDEX doesn't have a way to say PRIMARY KEY, so it's no
-	 * problem either.
+	 * If ALTER TABLE and CREATE TABLE .. PARTITION OF, check that there isn't
+	 * already a PRIMARY KEY.  In CREATE TABLE for an ordinary relations, we
+	 * have faith that the parser rejected multiple pkey clauses; and CREATE
+	 * INDEX doesn't have a way to say PRIMARY KEY, so it's no problem either.
 	 */
-	if (is_alter_table &&
+	if ((is_alter_table || heapRel->rd_rel->relispartition) &&
 		relationHasPrimaryKey(heapRel))
 	{
 		ereport(ERROR,
diff --git a/src/test/regress/expected/indexing.out b/src/test/regress/expected/indexing.out
index 8ab543ae31..225f4e9527 100644
--- a/src/test/regress/expected/indexing.out
+++ b/src/test/regress/expected/indexing.out
@@ -800,8 +800,24 @@ Indexes:
     "idxpart_pkey" PRIMARY KEY, btree (a)
 Number of partitions: 0
 
+-- multiple primary key on child should fail
+create table failpart partition of idxpart (b primary key) for values from (0) to (100);
+ERROR:  multiple primary keys for table "failpart" are not allowed
 drop table idxpart;
--- but not if you fail to use the full partition key
+-- primary key on child is okay if there's no PK in the parent, though
+create table idxpart (a int) partition by range (a);
+create table idxpart1pk partition of idxpart (a primary key) for values from (0) to (100);
+\d idxpart1pk
+             Table "public.idxpart1pk"
+ Column |  Type   | Collation | Nullable | Default 
+--------+---------+-----------+----------+---------
+ a      | integer |           | not null | 
+Partition of: idxpart FOR VALUES FROM (0) TO (100)
+Indexes:
+    "idxpart1pk_pkey" PRIMARY KEY, btree (a)
+
+drop table idxpart;
+-- Failing to use the full partition key is not allowed
 create table idxpart (a int unique, b int) partition by range (a, b);
 ERROR:  insufficient columns in UNIQUE constraint definition
 DETAIL:  UNIQUE constraint on table "idxpart" lacks column "b" which is part of the partition key.
diff --git a/src/test/regress/sql/indexing.sql b/src/test/regress/sql/indexing.sql
index 48b8853219..f145384fbc 100644
--- a/src/test/regress/sql/indexing.sql
+++ b/src/test/regress/sql/indexing.sql
@@ -401,9 +401,16 @@ drop table idxpart;
 -- Verify that it works to add primary key / unique to partitioned tables
 create table idxpart (a int primary key, b int) partition by range (a);
 \d idxpart
+-- multiple primary key on child should fail
+create table failpart partition of idxpart (b primary key) for values from (0) to (100);
+drop table idxpart;
+-- primary key on child is okay if there's no PK in the parent, though
+create table idxpart (a int) partition by range (a);
+create table idxpart1pk partition of idxpart (a primary key) for values from (0) to (100);
+\d idxpart1pk
 drop table idxpart;
 
--- but not if you fail to use the full partition key
+-- Failing to use the full partition key is not allowed
 create table idxpart (a int unique, b int) partition by range (a, b);
 create table idxpart (a int, b int unique) partition by range (a, b);
 create table idxpart (a int primary key, b int) partition by range (b, a);