"I'd say [his] season is in jeopardy," general manager Sandy Alderson said after the Mets beat Washington 4-2.
Alderson said the injury is "similar in location and severity to the one on the left side" Cespedes suffered in April. That setback put Cespedes on the disabled list on April 29 and the slugger didn't return until June 10.
Cespedes will be put on the DL and examined Monday in New York.
"I wouldn't necessarily expect it be as long, but we don't have that much time left in the season," Alderson said. "Very disappointing."
Cespedes has played in only 81 games this season due to various injuries. He is hitting .292 with 17 home runs and 42 RBIs for a team that has fallen out of playoff contention.
"Of course, I'm going to work hard and try to come back as soon as I can, but I'm not going to push myself to come back if I'm not 100 percent," Cespedes said through an interpreter.
The latest in a relentless string of injuries for the Mets occurred with Cespedes running the bases on what turned out to be a dead ball.
On second base with one out in the first inning, Cespedes took off on Dominic Smith's grounder up the middle. The ball squirted to the outfield after hitting second-base umpire Andy Fletcher, who immediately ruled the play over.
Cespedes rounded third base and immediately began hobbling, struggling to put weight on the right leg while laboring to home plate. He met with the New York training staff on the field before being removed.
"It's been very frustrating because I know how much work I put into this offseason to come in ready this season, probably more than ever before," Cespedes said.
"I've just had injury after injury. This one, in particular, is so frustrating because I think right before this I felt the best I've felt all season long. It's definitely frustrating."
New York lost outfielder Michael Conforto on Thursday with a dislocation and tear of his left shoulder.