The Spain international was carried off on a stretcher crying in pain following a late tackle from behind by Valencia's Enzo Perez who escaped a yellow card.
Barca said in a statement that Iniesta injured the lateral collateral ligaments in his right knee and would undergo further tests.
According to media reports, the 32-year-old will be out for two and a half months.
Barca coach Luis Enrique shouted at Perez when Iniesta went down and criticised referee Alberto Undiano Mallenco later for not booking the Argentine midfielder.
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"It was a clear foul ... and there was no yellow card," Luis Enrique said. "Tomorrow we'll find out the extent of the injury but it will be a number of weeks, it's a serious injury."
Undiano Mallenco's refereeing also angered Valencia.
The hosts protested against Lionel Messi's opening goal because Luis Suarez was in an offside position and interfering with play.
Valencia also appealed for a penalty when Samuel Umtiti barged Rodrigo Moreno in the area in the first half and were furious when Sergio Busquets was not shown a second yellow card.
"Undiano will be ashamed when he watches this game again," said sporting director Jesus Garcia Pitarch.
"There were three clear decisions in half an hour that went against us. Undiano needs to take a look at himself. Spanish football cannot afford to have such lamentable refereeing."
Valencia coach Cesare Prandelli said: "In Italy I never spoke about referees and I'm not going to now but the images are very clear and speak for themselves."
Messi's injury-time penalty settled an enthralling encounter while a bottle was thrown at Barcelona forward Neymar as the visitors celebrated the last-gasp winner.
Former Valencia striker Paco Alcacer also had an object thrown at him by a supporter while on the substitutes' bench.
"I'm not here to judge what the fans do, we just celebrated as you'd expect when you beat an opponent who have made things so difficult for you," said Luis Enrique.
(Editing by Tony Jimenez)
