The England international, who is on loan at Villa Park from Tottenham Hotspur, picked up the injury in September.
As a result he has been unable to make his debut for Villa.
However, the 28-year-old appears confident that he will make a return to the playing field shortly.
"On the train back to birmz," he wrote on his Twitter account.
"Got the all clear from the specialist to start my rehab so hopefully I'll be back playin soon!"
Jenas, who made his England debut in 2003, has gone on to represent his country on 21 occasions.