He will be examined further Wednesday.
Cruz said he felt better after getting treatment and hopes he won't be out long.
"I feel good right now," Cruz said after the Rangers' 4-3 loss. "We'll wait until tomorrow and see. Hopefully, it should be just one day."
Cruz said he felt the tightness trying to leg out a ground ball to third in the fourth inning and again on a fly ball to right in the sixth.
Mitch Moreland replaced Cruz in right in the seventh inning.
After a hot start, Cruz has struggled recently at the plate. He was 0-for-3 on Tuesday, making him 2-for-20 on this current road trip, dropping his average to .219 on the season.
He homered in each of the first four games this year but has gone deep only three times since then.
The slugger was on the disabled list three different times last season, all with hamstring issues. Cruz missed a total of 51 games with those injuries in 2010.
Richard Durrett covers the Rangers for ESPNDallas.com.