diff --git a/src/backend/optimizer/util/clauses.c b/src/backend/optimizer/util/clauses.c
index 5344f6167a..652843a146 100644
--- a/src/backend/optimizer/util/clauses.c
+++ b/src/backend/optimizer/util/clauses.c
@@ -1223,13 +1223,17 @@ max_parallel_hazard_walker(Node *node, max_parallel_hazard_context *context)
 
 	/*
 	 * We can't pass Params to workers at the moment either, so they are also
-	 * parallel-restricted, unless they are PARAM_EXEC Params listed in
-	 * safe_param_ids, meaning they could be generated within the worker.
+	 * parallel-restricted, unless they are PARAM_EXTERN Params or are
+	 * PARAM_EXEC Params listed in safe_param_ids, meaning they could be
+	 * generated within the worker.
 	 */
 	else if (IsA(node, Param))
 	{
 		Param	   *param = (Param *) node;
 
+		if (param->paramkind == PARAM_EXTERN)
+			return false;
+
 		if (param->paramkind != PARAM_EXEC ||
 			!list_member_int(context->safe_param_ids, param->paramid))
 		{
diff --git a/src/pl/plpgsql/src/pl_exec.c b/src/pl/plpgsql/src/pl_exec.c
index 9716697259..e605ec829e 100644
--- a/src/pl/plpgsql/src/pl_exec.c
+++ b/src/pl/plpgsql/src/pl_exec.c
@@ -6588,8 +6588,8 @@ exec_save_simple_expr(PLpgSQL_expr *expr, CachedPlan *cplan)
 	 * force_parallel_mode is on, the planner might've stuck a Gather node
 	 * atop that.  The simplest way to deal with this is to look through the
 	 * Gather node.  The Gather node's tlist would normally contain a Var
-	 * referencing the child node's output ... but setrefs.c might also have
-	 * copied a Const as-is.
+	 * referencing the child node's output, but it could also be a Param, or
+	 * it could be a Const that setrefs.c copied as-is.
 	 */
 	plan = stmt->planTree;
 	for (;;)
@@ -6616,9 +6616,9 @@ exec_save_simple_expr(PLpgSQL_expr *expr, CachedPlan *cplan)
 			/* If setrefs.c copied up a Const, no need to look further */
 			if (IsA(tle_expr, Const))
 				break;
-			/* Otherwise, it better be an outer Var */
-			Assert(IsA(tle_expr, Var));
-			Assert(((Var *) tle_expr)->varno == OUTER_VAR);
+			/* Otherwise, it had better be a Param or an outer Var */
+			Assert(IsA(tle_expr, Param) || (IsA(tle_expr, Var) &&
+					((Var *) tle_expr)->varno == OUTER_VAR));
 			/* Descend to the child node */
 			plan = plan->lefttree;
 		}
diff --git a/src/test/regress/expected/select_parallel.out b/src/test/regress/expected/select_parallel.out
index 2ae600f1bb..3c63ad1de8 100644
--- a/src/test/regress/expected/select_parallel.out
+++ b/src/test/regress/expected/select_parallel.out
@@ -101,6 +101,26 @@ explain (costs off)
          ->  Parallel Index Only Scan using tenk1_unique1 on tenk1
 (5 rows)
 
+-- test prepared statement
+prepare tenk1_count(integer) As select  count((unique1)) from tenk1 where hundred > $1;
+explain (costs off) execute tenk1_count(1);
+                  QUERY PLAN                  
+----------------------------------------------
+ Finalize Aggregate
+   ->  Gather
+         Workers Planned: 4
+         ->  Partial Aggregate
+               ->  Parallel Seq Scan on tenk1
+                     Filter: (hundred > 1)
+(6 rows)
+
+execute tenk1_count(1);
+ count 
+-------
+  9800
+(1 row)
+
+deallocate tenk1_count;
 -- test parallel plans for queries containing un-correlated subplans.
 alter table tenk2 set (parallel_workers = 0);
 explain (costs off)
diff --git a/src/test/regress/sql/select_parallel.sql b/src/test/regress/sql/select_parallel.sql
index 89fe80a35c..720495c811 100644
--- a/src/test/regress/sql/select_parallel.sql
+++ b/src/test/regress/sql/select_parallel.sql
@@ -39,6 +39,12 @@ explain (costs off)
 	select  sum(parallel_restricted(unique1)) from tenk1
 	group by(parallel_restricted(unique1));
 
+-- test prepared statement
+prepare tenk1_count(integer) As select  count((unique1)) from tenk1 where hundred > $1;
+explain (costs off) execute tenk1_count(1);
+execute tenk1_count(1);
+deallocate tenk1_count;
+
 -- test parallel plans for queries containing un-correlated subplans.
 alter table tenk2 set (parallel_workers = 0);
 explain (costs off)