The 30-year-old was carried off on a stretcher six minutes before half-time after appearing to land awkwardly.
The Catalan club confirmed soon after on their website, www.fcbarcelona.cat, that Spain's all-time record scorer had "suffered a fracture to the tibia in his left leg".
On Wednesday Barca coach Pep Guardiola dismissed Spanish media reports linking Villa with a move away from the Nou Camp in the January transfer window.
Sports newspaper Marca claimed the player was ready to move on from Barca just 19 months into the four-year deal agreed following his 40million euro transfer from Valencia.
The speculation over the Spain international's future appears to have sprung from Guardiola's decision to omit the forward from his starting line-up for Saturday's 3-1 Clasico victory against Real Madrid at the Bernabeu.
Marca - an openly pro-Real Madrid publication - suggested Villa had been made available for transfer and already touted to "the great English clubs, mainly Chelsea, Liverpool and Aston Villa", but Guardiola insisted the speculation was nonsense.
Speaking to reporters in Japan ahead of the Al Sadd game, Guardiola claimed: "Marca lie. I have not spoken to David after the last match in Madrid, but all of the players are in my plans.
"I am the one who comes up with 25 different line-ups during the season because I feel that is the best thing to do.
"Most of the players that are here now will continue for the rest of this season and the next."
Villa has scored five times in 15 Primera Division matches this season, following on from his 18 goals in 34 games as Barca won the league title last term. He has made 75 appearances for the club in all competitions, scoring 32 goals.