Barca won the match 4-0, with two goals from Adriano and one apiece from Seydou Keita and Maxwell, and will face Brazilian team Santos in Sunday's final.
Villa was carried off the field after injuring himself during a challenge late in the first half of Thursday's match.
Dr. Pedro Guilen, one of Spain's leading specialists in football injuries, told Radio Marca that he thinks Villa will be out of action for around six months.
Guillen also said he was sure that Villa will miss the Euro 2012 tournament, to be held in Poland and Ukraine in June.
"I am convinced that he will not go (to Euro 2012)," said Guillen.
Meanwhile, Alfonso del Corral, the former head of Real Madrid's medical services, told radio station Cadena COPE that Villa will be out for six months "even as an optimistic prediction. This is the usual time frame for an injury like this."
Villa was important in Spain's triumphs at the 2010 World Cup and at Euro 2008.
"Bad news for David Villa and Barca, the striker's left tibia is fractured," Barca said on its Twitter feed.
Barca said that the Spain striker had been taken to Yokohama's Rosa Hospital for further tests. Barca coach Pep Guardiola said after the game that Villa will return to Barcelona as soon as possible for surgery.
Villa did not start for Barca in the 3-1 Clasico defeat of Real Madrid last Saturday, which had provoked speculation about his future at the club and rumours about a possible departure.
He had complained about pain in his left leg since November.
Villa, 30, joined Barca from Valencia in 2010. He started his career at local club Sporting Gijon, before moving on to Zaragoza then Valencia.
The striker might not be the only Barca player missing from the final, because South Americans Alexis Sanchez and Javier Mascherano both finished the semi-final with pulled muscles.
