The 44-year-old stepped up from assistant to replace club hero Pep Guardiola at the end of last season, after having had surgery on a tumour in his saliva glands in November last year, and had made a record-breaking start to his tenure.
"While monitoring his parotid gland a change has been detected in his condition that requires surgery which will be carried out on Thursday," Barca said in a statement.
"His time in hospital will be about three to four days. During the period after his operation, depending on how he recovers, an attempt will be made to balance his treatment with his working life."
"Tito is the coach, and continues to be so," Zubizarreta said, dismissing rumours they may have tried to contact the out-of-work Guardiola.
"[Assistant] Jordi Roura will take charge against Valladolid. Tito I am sure will be watching us on television and wanting us to win."
Rosell added: "Tito has an incredible mental strength. He was worried for his family. This was his main concern. We have to leave them alone.
"Tito is the leader of the group, he won't be here for a few weeks, but we will continue working just the same."
The news of Vilanova's illness had been filtering out during the day after the club suddenly cancelled some scheduled events.
"Real Madrid wish to express their love and support to Barcelona coach Tito Vilanova, to whom we wish a prompt recovery," Barca's arch-rivals said in a statement.
"Real extend this support to the club and his family."
Former tennis world number one Rafa Nadal said: "All my strength and support for Tito Vilanova! We are all with you to overcome this next hurdle."
"I had an important operation a few months ago," he said. "I spoke with the medics and my family about the job, but they all said I was perfectly okay and there was no problem.
"Having overcome this operation it gives me a different view on life. Perhaps, after what has happened, training Barca will be like child's play."
