"The player received the green light to leave hospital (Wednesday evening) and is resting at home," it said, quoting the club's medical services.
His recovery "has been good, and he has shown no complications".
He will "recuperate at home and in four weeks he should be able to do some physical exercises, before returning to training with the squad", it said.
The 31-year-old French international underwent a three-hour operation on March 17 at a Barcelona hospital to remove the tumour.
A prolonged absence for the player would be a blow to Barcelona, who are in the final straight of another magnificent season.