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. He called it a "freak accident."
The 23-year-old right fielder said an MRI showed some damage and that he would be examined by a hand specialist.
Meadows is hitting .351 with six homers and 19 RBI in 20 games.
The Rays made several other roster moves on Sunday. They reinstated infielder Joey Wendle from the 10-day IL. Wendle, who missed 17 games because of a strained left hamstring, finished fourth in AL Rookie of the Year voting last season.
Reliever Emilio Pagan and infielder/outfielder Andrew Velazquez were recalled from Durham.