The Galaxy announced Barrett suffered the injury during a practice session Thursday.
Barrett had seven goals during the regular season and started the three Los Angeles playoff matches leading up to the MLS Cup. Landon Donovan leads the Galaxy in scoring with 12 goals.
Los Angeles will host Houston Sunday in the championship game.
Barrett came to Los Angeles this season after spending three years with Toronto and four with Chicago. His seven goals equaled his career single-season high.
Rosie O'Donnell unveils nearly 50-pound weight loss
Members of Congress to keep receiving porn magazine