The news also represents a setback for Spain as they prepare to defend their European Championships title in Poland and Ukraine next year.
"This injury is a tough blow but I am convinced I am going to recover quickly and am thinking about playing the [Champions League] final in Munich [in May]," Villa said on his Facebook page.
"I know my colleagues will get me there - and to Euro 2012. I'm going to work hard to achieve it."
Earlier in the day, club coach Pep Guardiola said: "David has fractured his leg and will return to Barcelona for an operation as soon as possible.
"We are all very sad for him. He's a charming personality and it's a massive blow for the team," added Guardiola after the European champions set up a final against Brazil's Santos.
Villa, Spain's all-time top scorer with 50 goals in 81 appearances, fell awkwardly in the first half and immediately signalled to the bench before he was rushed to a local hospital in Yokohama.
"He will be out for a long time," said Guardiola. "I don't know how long but it takes a long time to return after a break like this.
"All the players are very worried about David. We hope he will return as soon as possible. Our thoughts are with him and we will have to win the Club World Cup without him."
The Spanish champions later said they estimated Villa would be out for between four and five months.
VERY UNLUCKY
Villa's absence will narrow Guardiola's options as his side pursue titles in the Club World Cup, La Liga, Champions League and King's Cup.
Spain coach Vicente del Bosque was also concerned about the 30-year-old.
Villa was first-choice forward when Spain won the World Cup in South Africa last year and his national team partners Fernando Torres and Fernando Llorente are now struggling for form.
"It's very bad news, very unlucky for him," Del Bosque told Europa Press. "Thinking ahead to the European Championship it is obviously very bad news as well.
"There are still six months to go. Let's see how he recovers. Some return quickly, others take a little longer. First we need to listen to what the medics say."
Barca goalkeeper Victor Valdes said: "It's negative news on what should have been a special and historic day. We will try to dedicate the cup to him in the final."
Spain and Real Madrid defender Sergio Ramos said on Twitter: "A serious injury for national team colleague David Villa. Keep your spirits up and stay strong! Return soon champion..!!"
