diff --git a/src/backend/distributed/relay/relay_event_utility.c b/src/backend/distributed/relay/relay_event_utility.c
index 1643f82c6..7388ff383 100644
--- a/src/backend/distributed/relay/relay_event_utility.c
+++ b/src/backend/distributed/relay/relay_event_utility.c
@@ -158,7 +158,7 @@ RelayEventExtendNames(Node *parseTree, char *schemaName, uint64 shardId)
 												  AccessShareLock,
 												  missingOk);
 
-					if (constraint->contype == CONSTR_PRIMARY && constraint->indexname)
+					if (constraint->indexname)
 					{
 						char **indexName = &(constraint->indexname);
 						AppendShardIdToName(indexName, shardId);
diff --git a/src/test/regress/expected/multi_alter_table_add_constraints.out b/src/test/regress/expected/multi_alter_table_add_constraints.out
index 56ef04335..e96326c18 100644
--- a/src/test/regress/expected/multi_alter_table_add_constraints.out
+++ b/src/test/regress/expected/multi_alter_table_add_constraints.out
@@ -617,10 +617,23 @@ ORDER BY
  localhost |    57638 | t       |
 (2 rows)
 
+CREATE TABLE alter_add_unique(x int, y int);
+CREATE UNIQUE INDEX CONCURRENTLY alter_unique_idx ON alter_add_unique(x);
+SELECT create_distributed_table('alter_add_unique', 'x');
+ create_distributed_table
+---------------------------------------------------------------------
+
+(1 row)
+
+ALTER TABLE alter_add_unique ADD CONSTRAINT unique_constraint_test UNIQUE USING INDEX alter_unique_idx;
+NOTICE:  ALTER TABLE / ADD CONSTRAINT USING INDEX will rename index "alter_unique_idx" to "unique_constraint_test"
+ALTER TABLE alter_add_unique DROP CONSTRAINT unique_constraint_test;
 SET search_path TO 'public';
 DROP SCHEMA sc1 CASCADE;
 NOTICE:  drop cascades to table sc1.alter_add_prim_key
 DROP SCHEMA sc2 CASCADE;
 NOTICE:  drop cascades to table sc2.alter_add_prim_key
 DROP SCHEMA sc3 CASCADE;
-NOTICE:  drop cascades to table sc3.alter_add_prim_key
+NOTICE:  drop cascades to 2 other objects
+DETAIL:  drop cascades to table sc3.alter_add_prim_key
+drop cascades to table sc3.alter_add_unique
diff --git a/src/test/regress/sql/multi_alter_table_add_constraints.sql b/src/test/regress/sql/multi_alter_table_add_constraints.sql
index 3e80b09c0..612e4d22b 100644
--- a/src/test/regress/sql/multi_alter_table_add_constraints.sql
+++ b/src/test/regress/sql/multi_alter_table_add_constraints.sql
@@ -518,6 +518,13 @@ SELECT (run_command_on_workers($$
 ORDER BY
     1,2,3,4;
 
+CREATE TABLE alter_add_unique(x int, y int);
+CREATE UNIQUE INDEX CONCURRENTLY alter_unique_idx ON alter_add_unique(x);
+SELECT create_distributed_table('alter_add_unique', 'x');
+
+ALTER TABLE alter_add_unique ADD CONSTRAINT unique_constraint_test UNIQUE USING INDEX alter_unique_idx;
+ALTER TABLE alter_add_unique DROP CONSTRAINT unique_constraint_test;
+
 SET search_path TO 'public';
 
 DROP SCHEMA sc1 CASCADE;