Vardy, the Foxes' top-scorer this season with 17 Premier League goals, missed the 1-0 loss at Norwich last Friday due to a calf problem.
He will also sit out Leicester's FA Cup fifth-round clash with Birmingham on Wednesday night but Rodgers says he "should be fine" to face Villa five days later.
Asked about the 33-year-old striker on Monday, Rodgers was quoted by Leicester's official website as saying at his pre-match press conference: "No, he won't be available. He's making good progress but our target will be Villa and he should be fine for that."
Leicester's failure to score on Friday made it three successive games without a goal for Rodgers' men, part of a five-match winless run in all competitions.
Rodgers says it is the responsibility of all players in the side to score goals, not just Vardy, and he wants to see a response against Birmingham as they attempt to book their place in the quarter-finals of the FA Cup.
The game at Carrow Road saw midfielder Wilfred Ndidi return to action after a knee issue, coming on as a second-half substitute, and Rodgers says it is great news for the Foxes.
He got some much-needed minutes under his belt and looks set to face Pep Clotet's men on Wednesday night.
Ndidi has just the two goals to his name so far this season, and that is something the player and Rodgers will be hoping he can improve on now that he is back fit.
Leicester, third in the top flight, face a Birmingham outfit who are currently 15th in the Sky Bet Championship.
Clotet's side are unbeaten in their last 13 matches in all competitions and will prove to be stern opposition for the Foxes.