The former Hull defender has only made two starts for the Hoops since signing in July having previously spent months out with a ruptured cruciate ligament.
He was a free agent after his contract with Wolves was terminated by mutual consent in January.
Lennon said: "He was training on Monday and would have started tomorrow but he was going for the ball and we heard a pop.
"It's a rupture of his Achilles tendon. He's had surgery in France and we're waiting to hear how it went. We're looking at six months, so we are hoping to see him sometime in the New Year.
"This is a totally separate injury to the previous ones he had. It can happen to anyone at any time. He's had horrendous luck but we'll support him all the way.
"It is a devastating blow for him. I went in to see him and he was obviously really upset. He gave up his contract at Wolves to find a new club, came here on trial and impressed us."