The club hasn't ruled out Stanton being ready for Friday, but it will know more after he swings the bat on Wednesday.
The hand/wrist area was bothering Stanton enough to exit the game.
Stanton has been in contact with Marlins trainer Sean Cunningham, who is with the team in Atlanta.
"Again, I think it's the first time," Jennings said. "He's going to feel a little different. He just needs to be comfortable with it. Once he gets there, takes some batting practice and sees how it feels, strength-wise, then we'll know."
Stanton, who has 27 homers and 67 RBIs, was the National League Player of the Month in June. The right fielder was voted into the All-Star Game as a starter. But because of his injury, he didn't attend the event in Cincinnati.
The Marlins have been hopeful he will return for the Mets' series. But if he needs more time, then his status will remain unknown.
"He's going to test it today to determine the strength factor of where he is," manager Dan Jennings said. "Right now, it's one of those [situations where] we'll see how he is going and we'll go from there."
Stanton broke the bone in his hand on June 26 and had surgery two days later. Tuesday was his first game action since the injury. Stanton had three plate appearances, drawing a walk while also lifting a foul popout and a strikeout, looking.
The Marlins, gauging right-field options in case Stanton is out for a while, initially were planning on using Marcell Ozuna in right field on Wednesday and Ichiro Suzuki in center field.
But before Wednesday's first pitch, the team announced Ichiro would play right and Ozuna would go to center.
Ozuna, Miami's Opening Day center fielder, played four games in right last year, and he's played 40 games total there since his rookie season in 2013.