Injured while sprinting to first base on a ground ball in the 10th inning, Stanton will have an MRI taken on Tuesday.
"We'll find more in depth tomorrow," Stanton said. "But any time you go down, it's not good."
The Marlins are placing Stanton and first baseman Joe Mahoney, also with a right hamstring strain, on the disabled list. The team is recalling outfielder Marcell Ozuna from Double-A Jacksonville, and he will be making his MLB debut on Tuesday.
The Marlins used seven pitchers on Monday night, so to add depth to the bullpen, left-hander Brad Hand has been recalled from Triple-A New Orleans.
One reason Ozuna is getting the nod is because he already is on the 40-man roster. A power-hitting right fielder, Ozuna is batting .333 (14-for-42) with three doubles, a triple and five home runs at Jacksonville. He also has 15 RBIs in 10 games.
"He's on the roster," Marlins president of baseball operations Larry Beinfest said. "We just saw him play at Double-A. He's looked good. Defensively, he's very good. We have a choice of outfielders, but right now, Marcell is the guy."
Ozuna has power potential, and he is being asked to help fill the void for Miami being without Stanton, who was starting to heat up at the plate.
The 23-year-old Marlins slugger pulled up and stumbled after crossing first base on a groundout against the Mets at Marlins Park.
Facing Bobby Parnell, Stanton tapped a slow roller in front of the plate. In full sprint, the All-Star was thrown out. As he crossed first base, he reached for his right hamstring while tumbling to the ground.
Marlins trainer Sean Cunningham dashed out to check on the slugger, who out of frustration pounded the ground with his fist before walking off the field.
Off to a slow start, Stanton belted three homers in two games, including a pair against the Cubs on Sunday.
Stanton, 0-for-5 on Monday, is batting .227 with three home runs and nine RBIs.
"Obviously, we knew it was an injury that he was going to come back," manager Mike Redmond said. "We're enjoying this win tonight, but at the same time, tomorrow, the reality will set in that Stanton is not in the lineup anymore."
Greg Dobbs moved from first base to right field in the 11th inning, and Chris Valaika filled in at first base.
Earlier this season, Stanton missed five games with a bruised left shoulder.
"We're bringing up a young kid," Redmond said. "We're going to let him go out there and play. Ozuna is an exciting player. Hopefully, he will come up and provide a spark."