The injury had already ruled Fati out of Spain's upcoming games against Switzerland, Netherlands and Germany after he was named in Luis Enrique's squad last week. Real Madrid's Marco Asensio has been called up in his place.
Barca, meanwhile, will be without Fati until March, starting with their trip to unbeaten Atletico Madrid after the international break on Nov. 21.
Fati had made an excellent start to the new season after establishing himself as a regular under new coach Ronald Koeman. He has scored five goals in 10 appearances in all competitions and has also registered two assists.
In his debut campaign during the 2019-20 season, he became Barca's youngest ever scorer in La Liga, the youngest ever scorer in the Champions League and the youngest player to score for the Spain national team.
The loss of Ansu will be softened by the return of Philippe Coutinho after the international break. The Brazil international has missed Barca's last four games with a hamstring injury but could feature against Atletico.