Coach Kevin O'Neill says the sophomore will have surgery the week of Aug. 22 at USC Hospital.
Although Washington won't be able to play in games, he will travel with the Trojans on their trip to Brazil beginning Friday. They will play against Division I pro teams during the 10-day trip.
Washington appeared in three games last season without taking a shot. He had left shoulder instability at the start of last season, but the tear didn't happen until USC began practicing for its trip late last month.