Meadows was hurt when he awkwardly slid into third base on a two-run triple in the seventh inning of Saturday night's 6-5 loss to the Boston Red Sox. "Just kind of a freak accident," he said.
The 23-year-old right fielder said an MRI showed some damage and that he would be examined by a hand specialist.
"They don't know how bad the damage is," Meadows said. "It's pretty sore. Not sure if it's a ligament. We'll see where we're at."
Meadows is hitting .351 with six homers and 19 RBIs in 20 games.
"We got some crummy news on Austin Meadows," Rays manager Kevin Cash said. "What he's done for us has been pretty instrumental to us getting off to a hot start. Now we're going to need some other guys to kind of fill that void."
Tampa Bay began Sunday with a 14-7 record and in first place in the AL East.
Infielder Joey Wendle, who missed 17 games because of a strained left hamstring, was reinstated from the 10-day IL. He finished fourth in AL Rookie of the Year voting last season.
Reliever Hunter Wood was placed on the paternity list while reliever Jake Faria was optioned to Triple-A Durham.
Reliever Emilio Pagan and infielder/outfielder Andrew Velazquez were recalled from Durham.
Ace Blake Snell, on the 10-day IL with a fractured toe, likely will have a second bullpen session on Tuesday. The lefty threw 18 pitches off the mound Saturday.
A Tuesday throwing session would eliminate the possibility of the reigning AL Cy Young Award winner starting Wednesday against the Kansas City Royals, which initially was thought to be a possibility.
"I think he's slated to play catch a couple more days, probably have another bullpen and then figure out where we're going to put him back in," Cash said. "Everything has been real positive."
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