The 44-year-old Vilanova had a tumour removed from a salivary gland in his throat in November 2011 and in December 2012 he suffered a relapse.
He underwent surgery again followed by 10 weeks of chemotherapy and radiotherapy in New York. Vilanova returned to the helm of Barcelona in March and led the club to the Spanish league title.
"After evaluating the results of routine rests this week Tito Vilanova has been presented with the option of carrying out a treatment to continue to control his illness which will make it incompatible to carry out the role of first team coach from now on," Rosell told a news conference. "I want to ask everyone, especially the media, in the name of his family to show the maximum respect for the privacy of the whole process which will start now," he added.
Vilanova's replacement will be announced "probably in the beginning of next week," Rosell said.
Club officials met with the squad and the team decided they would not travel to Poland to face Lechia Gdansk in a pre-season friendly on Saturday, he added.
"I want to say that life goes on, this is a huge blow, a very hard blow, for Barcelona but Barcelona has suffered many blows and we have always overcome those blows and today will not be an exception," added Rosell, who was flanked by the club's sporting director Andoni Zubizarreta.
Several Barcelona players, including Argintine forward Lionel Messi and veteran defender Carles Puyol, attended the press conference in their kits.
Vilanova, who was under contract with Barcelona until June 2014, took over from Pep Guardiola as manager in June 2012, having previously worked as his assistant.
Last week Guardiola, who now coaches German and European champions Bayern Munich, accused Barcelona officials of using Vilanova's illness "to damage" him.
Without saying who exactly had made the accusation, Guardiola denied that he had missed a chance to visit Vilanova while he was being treated in New York for cancer. "I will never forget that they used Tito's illness to cause me damage, because it's a lie that I never saw him in New York," he said. Guardiola was living in New York at the time while on a year-long sabbatical after leaving Barcelona. Vilanova hit back at Guardiola's comments during Barcelona's first pre-season press conference on Tuesday, saying no one on the Barcelona board had used his illness to attack him.
"People aren't interested in personal matters, but Pep got it wrong and I'm surprised by his comments. No one on the board used my illness to attack him. The club tried to help me as much as possible," said Vilanova, who wore the collar of his white t-shirt raised so as to cover his neck.
"He visited me once in New York when I had just arrived, but during my recovery from the operation I was there for two months and I didn't see him. He's my friend and I needed him, but he wasn't there for me. I would have done things differently. I won't say anything else about this."
Barcelona are scheduled to face Bayern Munich in a friendly on Wednesday.