Syndergaard, 26, left his start against the Cardinals on Saturday night with the injury. He allowed four runs and struck out five in the Mets' 8-7 win.
Syndergaard was scheduled to undergo an MRI on Sunday morning. The Mets have not disclosed how long the 2016 National League All-Star will be out.
Syndergaard is 5-4 with a career-high 4.55 ERA this season. He has struck out 93 hitters in 95 innings.
New York entered play Sunday with a 34-36 record. The Mets trail the first-place Atlanta Braves by 6 1/2 games in the NL East Division.