Eyre, who's given up three earned runs in 4 1/3 innings this season, pitched a scoreless frame on Wednesday night before exiting while facing his first batter of the 10th inning, after re-aggravating the groin injury.
The 30-year-old right-hander opened this season on the DL with the same groin strain. Eyre also missed all of last season after undergoing Tommy John surgery in late 2007.
Rangers manager Ron Washington said Eyre's injury has proved tough because it was to the higher part of his groin, which is a difficult area to treat.
"I think Willie will let us know when he's ready, because you don't mess with the groin," Washington said. "Everything you do, the groin comes into play."
Mendoza joined the team in time for Thursday game's and Washington said the pitcher will be used primarily out of long relief in the bullpen.
The 25-year-old Mendoza has struggled with the Rangers during his two-year career, posting a 4-8 record with a 7.37 ERA. There is hope this season though, that Mendoza has left his past struggles behind.
During Spring Training, Mendoza worked on developing his breaking and offspeed pitches, and the early results have been good. The Mexico native posted a 3.86 ERA through four games with the Rangers during Spring Training, before being optioned to their farm system on March 24.
His success carried into the season as he was named the Pacific Coast League Pitcher of the Week for April 9-19, having gone 2-0 while tossing 10 1/3 scoreless innings over two Minor League starts so far this year.
"Hopefully he's gotten through everything and he can come up here and throw the ball the way he threw in Triple-A," said Washington. "If he does, that's another one of our young pieces that we've got."
Alden Gonzalez is a reporter for MLB.com. David Singh is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.