The team said in a statement that Smart was diagnosed with a Grade 1 tear of his left medial gastrocnemius. According to the Celtics, he is expected to return in two to three weeks.
ESPN reported Sunday that Boston is optimistic Smart could return in closer to one to two weeks.
Smart underwent an MRI on Sunday after exiting in the fourth quarter of the Celtics' 96-95 loss to the Los Angeles Lakers on Saturday. He departed the game after collapsing near Boston's bench following a rebound.
After the Celtics called a timeout, Smart remained down on the court momentarily before eventually being helped to the locker room. He was unable to put any weight on his left leg while being assisted off the court.
Smart entered Saturday's game averaging 13.2 points and six assists per game -- both career highs.
The Celtics, who have lost two consecutive games, leave Monday for a five-game road swing starting Tuesday in San Francisco against the Golden State Warriors.