According to Mike Puma of the New York Post, Conforto clutched his shoulder after swinging and missing on a pitch from Robbie Ray in the bottom of the fifth inning.
As the Mets have tumbled down the standings in the National League, injuries to key players have continued to mount.
Yoenis Cespedes, Noah Syndergaard, Matt Harvey, Jeurys Familia, David Wright and Neil Walker have all missed time due to injuries this season.
Conforto has been one of New York's few consistent presences in the lineup, though he did injure his wrist after being hit by a pitch against the San Francisco Giants on June 25. He's been putting up career-best numbers with a .279 batting average, 27 home runs and 68 RBI this season.
The 24-year-old was named an All-Star for the first time this season as well.
Brandon Nimmo replaced Conforto after he exited Thursday. He likely will continue to fill in as the right fielder for as long as Conforto is out, with Juan Lagares playing center.