A team has finished a game with 16-0 runs on that many hits 6 times since 1897, most recently Cleveland Buckeyes on 23 July 1947. That is about one every 73,834 team-games.
Box score for the most recent one ↗
13-0 13-1 14-0 14-1 14-2 15-0 16-0 16-2 16-4 17-0 18-0 19-0 20-0