The club, who announced the rescheduled operation on their website, have not released details about the kind of tumour the 31-year-old French international has and it remains unclear how long he will be out of action.
His absence for any length of time will be a severe blow to the La Liga leaders, who are five points ahead of Real Madrid with 10 games left, given his superb form this season and their relatively small squad.
Barca also have a chance of repeating the unprecedented treble they won in the 2008/09 season as they are through to the Champions League quarter-finals and play Real Madrid in the final of Spain's King's Cup on April 20.
The versatile Abidal, one of the most popular players with Barca fans, normally plays at left-back but has filled in brilliantly in central defence when regulars Carles Puyol and Gerard Pique have been absent.
"This is the toughest moment I have experienced in a dressng room," midfielder Xavi said at a news conference on Wednesday after Abidal visited the squad at training as they prepared for this weekend's game at home to Getafe.
"But Abidal will get through it because he is one of the strongest people mentally that I know," Xavi said.
"He is a paragon of optimism. He told us that life is like that, that we should carry on as normal and that we should beat Getafe on Saturday."
TWITTER MESSAGES
A host of La Liga players, including Real forward Cristiano Ronaldo, sent Abidal messages of support via their Twitter feeds after Barca announced he needed surgery on Tuesday.
Club president Sandro Rosell said on Wednesday Barca would do everything in their power to help the player recover.
"Barca is 100 percent behind Eric Abidal," Rosell told fcbarcelona.cat. "Health is more important than anything else in life," he added. "Abi, Barca loves you."
Abidal joined the Catalan club from Olympique Lyon in 2007 and has also played for Ligue 1 sides Lille and AS Monaco.
He has made 52 appearances for France, including in the 2006 World Cup final against Italy when he netted a penalty in the shootout that the Italians won 5-3.
Xavi said he could not understand why European governing body UEFA had decided Real and Lyon should not be allowed to wear shirts with a message of support for Abidal at their Champions League match at the Bernabeu later on Wednesday.
"It seems a bit insensitive," he said. "There are much more important things in life than football."
