The Dolphins believe Cutler suffered two cracked ribs and could be sidelined for two to three weeks, a source told ESPN's Adam Schefter.
Dolphins head coach Adam Gase was noncommittal on his starting quarterback for Thursday's game against theBaltimore Ravensuntil further evaluation.
"Right now they're going to take him to get a MRI, X-ray, figure out what it is, confirm," Gase said. "They have an idea. I didn't really get into it with them. It's something with his chest -- the chest and ribs area."
Cutler took a shot from Jets outside linebacker Jordan Jenkins early in the third quarter and was helped to the sideline. Cutler was taken into the locker room soon after for further evaluation.
Moore entered the game and threw for two touchdowns in Cutler's absence, rallying the Dolphins from a 14-point fourth-quarter deficit.
Moore finished the game 13-of-21 for 188 yards and the two touchdowns. He also threw an interception. Before he was injured, Cutler was 12-of-16 for 138 yards with two touchdowns and one interception.
Left tackle Laremy Tunsil also left Sunday's game in the third quarter with an injury to his left knee.
The Dolphins are no stranger to quarterback injuries. Former starting quarterback Ryan Tannehill suffered a season-ending knee injury in August, which spurred Miami to sign Cutler out of retirement with a one-year, $10 million contract.