The team announced Wright had a Grade 2 strain of the hamstring, the middle of three levels, after undergoing an MRI at the Hospital for Special Surgery in Manhattan. Mets manager Terry Collins estimated Wright would miss three to five weeks.
Wright was forced to depart Friday night's game against the Kansas City Royals after beating out an infield single in the 10th inning.
Wright had been battling hamstring discomfort for a week, although the organization portrayed the issue as a cramp and insisted the third baseman was not exercising poor judgment in playing through the injury.
"There are certain guys you almost can't afford to lose," Collins said. "He would fit that category for us."
Wright said he wanted to keep himself under control running out the grounder in the 10th inning when the hamstring finally gave out Friday night, but his hustling instincts kicked in.
He portrayed the injury as unavoidable. He added that it is not his style to have rested for a prolonged period when the issue initially arose a week ago in Washington. Sitting out for several days then might have avoided a greater absence now.
"I obviously felt it in Washington [last weekend] and got that day off on Sunday and felt it again in Miami the next series," Wright said. "So whether it was last night or a week from now, I think it was somewhat inevitable.
"You just have this mindset that I tried to keep myself under control. You just try to keep it at 75, 80 percent. And you just can't play that way. You see the ball, an infield single, and you want to try to beat it out. You put your head down and the next thing you know what happened, happened.
"It's just one of those things. I don't think it could have been prevented, unless the first time you feel it you go directly to the DL. That's not going to happen. I think that this was inevitable."
Collins added that Friday was a particularly tough day injury-wise for the Mets. Closer Bobby Parnell was prescribed medication and remained unavailable because of neck discomfort, while lefty specialist Josh Edgin landed on the DL with a hairline fracture of a rib on his left side.
The Mets promoted outfielder Mike Baxter from Triple-A Las Vegas to take Wright's roster spot.
Collins had another concern: Who will fill Wright's No. 3 slot in the batting order? Satin found himself there Saturday, although that is only because the Mets were facing a left-handed pitcher, Bruce Chen.
Wright, 30, is hitting .309 with 16 homers and 54 RBIs and has a .391 on-base percentage this season. The Mets rank second-to-last in the National League with a .238 team batting average.
"Somebody has to hit third," Collins said. "That's another hole to fill."
This is only the third DL trip for Wright in his 10-year major league career. He missed two weeks in 2009 with a concussion after getting beaned by a fastball from San Francisco's Matt Cain. He missed two months in 2011 with a stress fracture in his lower back, after playing through the injury for weeks.
Wright, who earned the nickname "Captain America" for his performance in the World Baseball Classic in March, ultimately had to withdraw from the tournament because of a rib-cage injury, although he was ready for Opening Day.