The Spain international was admitted to Barcelona Hospital on Monday but has been discharged a day later following treatment.
"David Villa was admitted on Monday to the Hospital of Barcelona, because of a renal colic. The player has been subjected to appropriate treatment to remove kidney stones on Tuesday and has already been discharged from hospital," a statement on Barcelona's official website read. "Villa will rejoin training this Wednesday and could be available for the next game against Granada."
The former Valencia forward has failed to hold down a regular place in Tito Vilanova's starting XI since making his return from a broken leg, but he started and scored for Barcelona in the club's 6-1 rout of Getafe over the weekend.