Lagares, a Gold Glove winner in 2014, hyperextended the big toe on his left foot and tore a ligament Wednesday when he raced to catch a drive by Toronto Blue Jays third baseman Gio Urshela in the ninth inning.
Surgery has tentatively been scheduled for next week, the team said.
An elite defender who starts regularly against left-handed pitching, Lagares was off to a fine start at the plate this season, hitting .339 with no homers and six RBIs in 59 at-bats. He also had three stolen bases.
Lagares had figured to get more playing time while Yoenis Cespedes (hip) is sidelined.
Information from the Associated Press was used in this report.