The injury had initially been termed "tightness," per Dodger Insider.
He exited the contest after just 15 pitches and one inning of work.
Hill has been plagued by injuries through the years, and blisters on his pitching hand have been the biggest hindrance. He has averaged just 23 starts over the last three seasons.
The 15-year veteran has thrown more than 136 innings just once in his career, tossing 195 innings while making 32 starts for the Chicago Cubs in 2007.
Hill missed the start of the 2019 campaign after suffering a medial collateral ligament strain in his left knee during spring training.
When he has been healthy, though, he has helped provide the Dodgers with solid depth behind ace Clayton Kershaw. He entered Wednesday night's game with a 30-16 record and a 3.20 ERA in 65 career outings for L.A. During his first nine starts of 2019, he went 4-1 with a 2.60 ERA.
Hill had been in a groove, going 3-0 with a 2.37 ERA and .239 average against in his three previous June starts. The 39-year-old has not allowed more than three earned runs in an outing this season and has not lost a start since May 9.
As long as Clayton Kershaw, Hyun-Jin Ryu, Walker Buehler and Kenta Maeda remain healthy, the Dodgers should be able to withstand a Hill injury as they attempt to reach the postseason for a seventh consecutive season. Former top prospect Julio Urias is currently in the bullpen and could be an option for the rotation should Hill miss time.