The announcement came a day after he dislocated his left thumb in the fifth inning of the Rays' 2-0 victory over the Seattle Mariners at Safeco Field.
Zobrist was caught stealing at second base and made awkward contact with the bag on a headfirst slide. He winced in pain before leaving the game and was replaced by utility player Sean Rodriguez.
"Best-case scenario would be that it heals very quickly, and I can get back on the field, I don't know, maybe within a week," Zobrist told reporters Wednesday in Seattle. "But that's unlikely."
Zobrist, a two-time All-Star, is hitting .260 with three home runs and nine RBI in 40 games this season.
Infielder Cole Figueroa was added from Triple-A Durham to take Zobrist's place on the roster. Figueroa, who was hitting .299 with three homers and 16 RBI in 33 games for the Bulls, is making his first trip to the majors.