The team recalled left-handed reliever Sean Gilmartin from Triple-A Las Vegas in a corresponding move.
"They didn't really see a lot,'' manager Terry Collins said of Cespedes' MRI. "It's probably better news than we thought. It's still going to be a while, obviously, but it's in a different part of [the hamstring] where the injury was last week.''
Collins also said pitcher Noah Syndergaard tossed Friday afternoon and could potentially pitch again as early as Sunday if the right-hander reported no discomfort. Syndergaard was scratched from his start Thursday because of biceps and shoulder discomfort.
The Mets are expected to send Cespedes to Florida for rehab, sources told ESPN's Buster Olney. He could receive platelet-rich plasma injections.
The outfielder had to exit the team's 7-5 defeat to the Atlanta Braves on Thursday. It was the Mets' sixth straight loss. New York is in last place in the NL East with an 8-13 record.
Cespedes pulled up lame after rounding first base on a one-hop double in the bottom of the fourth inning. He bent over in pain after reaching second as Collins and head athletic trainer Ray Ramirez rushed out to see what was wrong.
Cespedes draped one arm over the shoulder of Ramirez and the other over the shoulder of first-base coach Tom Goodwin as he limped slowly back to the Mets dugout.
Cespedes, 31, who has six home runs and 10 RBIs this season, had just returned to the lineup Wednesday after a nagging hamstring injury had sidelined him for three games.
The Associated Press contributed to this report.