Lagares hurt the thumb in the fifth inning when he came up short on Anthony Rendon's bloop single.
The former Gold Glover didn't indicate at first he was hurt, but manager Terry Collins and a trainer went to check on him in the outfield one batter later. Lagares was replaced by pinch hitter Curtis Granderson in the bottom of the fifth.
Lagares played because outfielder Michael Conforto missed his fourth straight start with a stiff back.
Collins said he wasn't surprised when a trainer told him Lagares had snapped the thumb on his glove hand, given how many injuries the Mets have had this season.
"That's kind of my thought. How many can we possibly continue to have to play through?'' Collins said. "But you know what the answer is? As many as pop up. That's how many you've got to play through.''
The Associated Press contributed to this report.