The 34-year-old defender, who has suffered a series of injuries over the past year, had arthoscopic surgery on his right knee in the Catalan capital on Thursday.
"Carles Puyol underwent an arthroscopy on Thursday evening in order to clean up his right knee," said a club statement.
"Puyol's return will be determined by the progress of his recovery."
Puyol had already been overlooked for Spain's World Cup qualifiers against Finland and France later this month.
Barcelona travel to Paris for the first leg of their last-eight tie on 2 April, with the return at the Nou Camp eight days later.