The Spain striker has been linked with a move away from the Nou Camp after finding first-team opportunities limited this season following his recovery from a serious leg injury, with Arsenal one of the clubs believed to be interested in the 31-year-old.
However, Barca have consistently dismissed suggestions Villa could be sold during the January transfer window and Vilanova repeated that stance following his side's 3-1 victory over Malaga on Sunday night.
He told reporters: "David is not going to leave. We are very happy with him."
Villa scored a brace in last week's 5-0 Copa del Rey win over Cordoba but limped out of the match late on and then picked up a hamstring injury in training on Saturday which ruled him out of the trip to Malaga.
Spain's record goalscorer missed much of last season and Euro 2012 after breaking his leg at the FIFA Club World Cup in December, 2011.
Vilanova added: "The other day he scored two goals. We've always said that he's coming off a long injury, and he's getting more minutes all the time. But he's suffering more physical problems again.
"We know how important he is, like last year when we missed him a lot in the second half of the season.
"I'm convinced he will help us a lot over the remainder of the season."