Adriano scored a first-half brace as Barcelona demonstrated its dominance, but the injury to Villa late in the opening half was later revealed as a fractured tibia that leaves his season in doubt.
Villa is Spain's all-time leading scorer, and played an integral role in both the Euro 2008 and 2010 World Cup triumphs for his country.
Although he played a lesser role for Barca this season, he scored 30 goals for the club last season. His injury could rule him out for the rest of the club season, as well as next summer's Euro 2012 finals.
Seydou Keita and Maxwell added second-half goals for Barca in the easy win, as it advanced to Sunday's final to play South American champion Santos.
Al-Sadd will play Japanese side Kashiwa Reysol in the third-place game Sunday.