Grimm allowed seven runs in the first two innings but was still in the game in the fourth when Miguel Cabrera singled with one out. The rookie right-hander threw one pitch to Prince Fielder and appeared to grimace, and after a brief conference on the mound, Joe Ortiz came on in relief.
The Tigers were ahead 7-2 when Grimm left. He allowed 10 hits in 3 1-3 innings.
"We'll have to see, but that was his last start before the break, so we'll have some time to get him OK," Rangers manager Ron Washington said.
Texas recently put Yu Darvish on the disabled list with a bad back. Four starters from the Rangers' season-opening rotation are currently on the DL.
Information from The Associated Press was used in this report.