The Mets recalled utility man Eric Campbell from Triple-A Las Vegas as a roster replacement.
Wright was injured when he slid into second base on a steal attempt in the eighth inning of New York's 6-5 victory. He walked off the field under his own power.
Mets manager Terry Collins said after the game that Wright's hamstring injury is a "major problem."
"Anytime you feel something like that, you hope that it goes away," Wright said to MLB.com. "This just didn't go away. Real frustrating. I pride myself on going out there and trying to play every day, and this just sucks."
Catcher Anthony Recker replaced Wright at third base in the ninth inning as New York dealt with a short bench. Outfielder Michael Cuddyer previously left the game after sustaining a contusion on his hand from being hit by a pitch.
Wright is batting .333 with one home run and four RBI in eight games this season for the Mets (5-3).
- Molly Geary and Scooby Axson