The 28-year-old was stretchered off in the eighth minute following a challenge from Gonzalo Escalante, and test results confirmed the midfielder has sprained an external lateral ligament.
The timing of his return will depend on the recovery, however reports in Spain suggest he is likely to be sidelined for at least two weeks, ruling him out of the Copa del Rey quarter-final second leg with Real Sociedad on Thursday.
He could also miss the next two LaLiga fixtures against Real Betis and Athletic Bilbao, but Barcelona coach Luis Enrique will be hoping the Spaniard is fully fit for the Champions League last-16 first-leg tie with PSG on February 14.
In the meantime though, Luis Enrique is optimistic he has the resources available to cope with the Spaniard's absence, in what is a busy period for the club.
"Busquets' injury is not as serious as we thought and we claimed a very good result," he said.
"Sergi Roberto, [Ivan Rakitic] and [Javier Mascherano] can play there [in Busquets' position]. I will not complain that I have all the cards.
"I like Rakitic in the pivot position. He was especially good and I have also liked Arda [Turan]. They all contribute things to the benefit of the team."