diff --git a/doc/src/sgml/ref/reindex.sgml b/doc/src/sgml/ref/reindex.sgml
index 1c21fafb80..47cef987d4 100644
--- a/doc/src/sgml/ref/reindex.sgml
+++ b/doc/src/sgml/ref/reindex.sgml
@@ -225,10 +225,15 @@ REINDEX [ ( VERBOSE ) ] { INDEX | TABLE | SCHEMA | DATABASE | SYSTEM } <replacea
 
   <para>
    Reindexing a single index or table requires being the owner of that
-   index or table.  Reindexing a database requires being the owner of
-   the database (note that the owner can therefore rebuild indexes of
-   tables owned by other users).  Of course, superusers can always
-   reindex anything.
+   index or table.  Reindexing a schema or database requires being the
+   owner of that schema or database.  Note that is therefore sometimes
+   possible for non-superusers to rebuild indexes of tables owned by
+   other users.  However, as a special exception, when
+   <command>REINDEX DATABASE</command>, <command>REINDEX SCHEMA</command>
+   or <command>REINDEX SYSTEM</command> is issued by a non-superuser,
+   indexes on shared catalogs will be skipped unless the user owns the
+   catalog (which typically won't be the case).  Of course, superusers
+   can always reindex anything.
   </para>
 
   <para>
diff --git a/src/backend/commands/indexcmds.c b/src/backend/commands/indexcmds.c
index b9dad9672e..d54c78c352 100644
--- a/src/backend/commands/indexcmds.c
+++ b/src/backend/commands/indexcmds.c
@@ -2415,6 +2415,18 @@ ReindexMultipleTables(const char *objectName, ReindexObjectType objectKind,
 			!IsSystemClass(relid, classtuple))
 			continue;
 
+		/*
+		 * The table can be reindexed if the user is superuser, the table
+		 * owner, or the database/schema owner (but in the latter case, only
+		 * if it's not a shared relation).  pg_class_ownercheck includes the
+		 * superuser case, and depending on objectKind we already know that
+		 * the user has permission to run REINDEX on this database or schema
+		 * per the permission checks at the beginning of this routine.
+		 */
+		if (classtuple->relisshared &&
+			!pg_class_ownercheck(relid, GetUserId()))
+			continue;
+
 		/* Save the list of relation OIDs in private context */
 		old = MemoryContextSwitchTo(private_context);