Avila remained in the game and caught the first four innings before Bryan Holaday replaced him to start the fifth.
"He doesn't want to come out of the game," Tigers manager Brad Ausmus. "Quite frankly, I don't want to take him out of the game. He's working with [winning pitcher] Rick Porcello. I don't like removing catchers when we have a lead and they're working with the starting pitcher."
Ausmus said he would give Avila a day off on Saturday, but he didn't expect the injury to become a long-term issue.
Avila went 1-for-2 at the plate and scored on Ian Kinsler's single in a seven-run third inning.
Patrick Donnelly is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.