Villa was vying with two defenders in the 37th minute when he landed awkwardly. The Spanish star immediately fell to the ground and called for help. He was carried off the pitch on a stretcher.
Barcelona said on its website that Villa had been taken to hospital for tests.
“Missing him in the team is going to be a blow,” Barcelona coach Pep Guardiola said. “I understand it is going to be a long time. We all love David. His personality is great. We all worry about him.”
Villa is Spain’s all-time leading scorer and helped the team with the 2008 European Championship and 2010 World Cup.
Spain coach Vicente del Bosque was devastated by word of Villa’s injury but remained hopeful that the striker might recover in time for the 2012 European Championship beginning in June.
“The news is very bad,” Del Bosque was quoted as saying by Spanish news agency Europa Press. “It’s a great misfortune, for him above all since he is the injured one, and looking ahead to the Eurocup (Euro 2012), of course this is very bad news.
“There are six months to go. Let’s see if he can get well. Recovering always has its set processes, but there are some players that get healthy sooner than others.”
After a 4-0 win over Al Sadd, Barcelona will play South American champion Santos in the Club World Cup final with the chance to lift its 13th trophy under Guardiola.
“This is very bad news on what was supposed to be a happy day moving on to a historic final,” said Barcelona goalkeeper Victor Valdes, who added that the team would dedicate the title to Villa if they win.
Villa scored 23 goals last season, his first with Barcelona. The 30-year-old Villa has seen his playing time diminish this season with the arrival of Cesc Fabregas and Alexis Sanchez, but he has still scored eight goals.
While he is no longer a certain starter for Barcelona, he remains an integral part of the Spain lineup. Spain will seek to defend its title at Euro 2012 in Poland and Ukraine.
The possible loss of Villa would leave Spain coach Vicente del Bosque with out-of-form Chelsea striker Fernando Torres, Athletic Bilbao’s Fernando Llorente and Sevilla’s Alvaro Negredo competing for places up front. In-form Valencia scorer Roberto Soldado would be Villa’s likely replacement if he doesn’t recover in time.
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