A team has finished a game with 17-1 singles and extra-base hits 66 times since 1897, most recently Colorado Rockies on 24 June 2010. That is about one every 6,712 team-games.
Box score for the most recent one ↗
16-8 16-9 16-10 16-11 16-12 17-0 17-1 17-2 17-3 17-4 17-5 17-6 17-7
The whole distribution — Singles and Extra-Base Hits · All 18 shapes