He made his season debut on Wednesday against the Washington Nationals and lasted only one inning after he was hurt chasing a fly ball in the top of the first. He originally was hurt last weekend in an exhibition game in Montreal.
Young signed a one-year, $7.25 million deal with the Mets in the offseason after spending 2013 with the Oakland Athletics. He spent his first seven seasons with the Arizona Diamondbacks.
"It feels like a bad dream," Young said. "It's the last way you want to come with a new team. I feel terrible about it."