"The plan right now is [Friday in] New York," Upton said after the Rays' 3-0 loss. "[I] can't really gauge anything right now. [We'll] see how it feels tomorrow and then go from there."
The injury occurred in the first inning, when Upton gave chase to David Ortiz's RBI double.
"[It's] tough to say when it happened, but it was definitely on that play," Upton said. "It didn't feel too bad at the time. Once the game went on it just kind of got stiffer and stiffer, and I felt like if I had to run hard it was going to go. So, pretty much now is not the time for that."
With Upton joining Evan Longoria and Carl Crawford on the shelf, Rays manager Joe Maddon said the roster was getting a little "thin" and suggested after Monday night's game that they could be getting help from their farm system in the next day or two.
Upton already has been dealing with pain as he has been playing with an injury to the labrum in his left shoulder, which has caused him to quit taking batting practice.
Fernando Perez moved over from left field in the bottom of the fifth to take Upton's place in center field. Ben Zobrist was inserted into the game in left field to take Upton's spot in the lineup.
Upton entered Monday night's game hitting .275 with eight home runs with 64 RBIs.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.