Vilanova underwent surgery on Dec. 20, a day after the club announced that the 44-year-old's condition had returned. He first had treatment in 2011.
"He'll be back within 15 or 20 days, but he must spend some days at the hospital and rest," Rosell told reporters in Dubai on Friday.
"He will mix work with his treatment. The most important thing is his health. Right now football comes second," added Rosell.
Barcelona have made a record-breaking start to their first season under Vilanova, who replaced friend Pep Guardiola at the helm at the end of the last term, by dropping only two points in 17 matches to lead La Liga by nine points.
Assistant Jordi Roura is taking charge in his absence. Barca's next league match is at home to city rivals Espanyol on Jan. 6.