Wright underwent an MRI on Saturday morning before the Mets hosted the Kansas City Royals hours later. Wright came up lame as he sprinted to first base in the 10th inning of Friday's 4-2 win by New York.
"There are certain guys you really almost can't afford to lose," Mets manager Terry Collins said Saturday. "He would fit that category for us.
"David Wright is a star and you're going to miss his presence in your lineup. Any team that loses their number one player, it's a huge hole to fill."
The Mets recalled outfielder Mike Baxter from Triple-A Las Vegas, and he arrived in New York on Saturday morning from Nashville, where the minor league club is playing.
Wright had been feeling discomfort in the hamstring while the Mets took on the Marlins in Miami this week, but it was described as cramping, and he played through it.
Now he will be sidelined for at least 15 days, but no timetable has been announced yet by the Mets.
He offered little resistance when he was removed from the game after being attended to behind first base.
Justin Turner took Wright's place at third base Saturday, and first baseman Josh Satin filled his No. 3 slot in the batting order.
Collins wouldn't commit to any plan beyond Saturday.
"We may have to make some lineup adjustments if it's going to be a long-term thing," he said. "If it's going to be two weeks, maybe we can just buy some time with some other guys."
One possibility Collins offered is moving Daniel Murphy from second base back to third, which might be his best position.
"Somebody has got to hit third on this team, too," Collins said. "That's another hole to fill. Somebody has got to do it. You can't sit there on a daily basis and say, 'Gee, David is not here.' We know he's not here.
"We're not asking anybody to try to be David. They've got to be themselves, but somebody has got to hit in those lineups. We just can't leave it blank."
Baxter was sent down to Las Vegas, along with first baseman Ike Davis on June 9 when Satin was called up. Davis has also since returned to the Mets.
Baxter batted .212 with no home runs and four RBIs in 85 at-bats over 41 games with the Mets earlier this season.
"Any time you get sent down you're always hoping you get a chance to come back. You don't take that for granted," Baxter said. "I really wish it wasn't on these terms. Watching David getting hurt last night, nobody really wants to see that. He is the heart of this team.
"Somebody is going to have to step up and we're going to have to try to pick up the slack for him. It's a big hole to fill. I don't know if one guy can do it. It's probably going to have to come from a couple of us. Hopefully we do."
The Mets were already dealing with multiple injuries in the bullpen on Friday before Wright got hurt.
New York closer Bobby Parnell is unavailable until at least Sunday because of a stiff neck. Left-handed setup man Josh Edgin went on the disabled list Friday, and is expected to be sidelined four to six weeks because of a stress fracture in a rib.
Veteran reliever Pedro Feliciano was brought up on Friday from Las Vegas and he made his first major league appearance since 2010.
Carlos Torres, who was scheduled to be Saturday's starter, was returned to the bullpen Friday, and he earned the win with a two-inning effort. He will stay as a reliever for now because the Mets are abandoning their six-man rotation until Jonathan Niese returns soon from a shoulder injury.
Jeremy Hefner was moved up from his Sunday start to pitch in Torres' place against the Royals on Saturday. Zack Wheeler, used as a pinch runner on Friday, will take the mound Sunday afternoon.