After being hit by two pitches in his first two plate appearances, Damon left the series finale against the Twins with a contusion on his left hand.
Liriano hit Damon to lead off the game and hit him again to begin the third inning. Damon was hit on his left hand the second time, and it was noticeably swollen after the Rays' 12-5 victory.
"It's definitely a day-to-day thing," Rays manager Joe Maddon said Wednesday. "We'll reevaluate tomorrow. But for right now, there's a chance -- more than likely not tomorrow, but maybe the day after that, or Saturday -- that he'd be able to play."
Damon remained in the game to run the bases in the third, and the veteran designated hitter said he tried to ice his hand and keep the swelling down to stay in the game. Damon was replaced before he was due up in the fourth, as Sam Fuld batted for Damon and walked.
Now, Damon is just hoping the injury only lasts a couple days and doesn't keep him out until the All-Star break.
"I got lucky," Damon said. "One inch either way, it could be really bad."
Rays catcher Kelly Shoppach, who also was Damon's teammate in 2005 with the Red Sox, said he expects Damon back in the lineup sooner rather than later.
"He'll be in there [Thursday]," Shoppach said. "Come on, it's Johnny Damon -- 15 straight years, 140-plus games. It won't be long, if it's long at all.
"I watched this guy once run into the fence in Fenway, slit his eyelid, had to have stitches on his eyelid -- played the next day."