Jenas joined Villa on loan from Tottenham over the summer.
Villa has confirmed that the 28-year-old midfielder has undergone a successful operation on his injured Achilles.
“This is tragic for Jermaine and, of course, we are all deeply disappointed for him,” Villa boss Alex McLeish told the club’s official website.
“To lose a player of his talent and experience is bad enough but to have never seen him play enough in a Villa shirt for our fans to appreciate the player he is, that’s terrible bad luck.
“Obviously, we wish Jermaine as speedy a recovery as possible and a full recovery too.
“He has been a great professional to have at the club since he arrived on loan in August.”
