The 26-year-old Biarritz player, capped nine times by his country, was a revelation at last year's World Cup and his absence further depletes France's second row.
Captain Fabien Pelous remains doubtful with a knee injury, Olivier Brouzet is still struggling with the shoulder problem he sustained in Australia and there are also concerns over the fitness of David Auradou.
"Jerome underwent examinations on Monday which revealed their was a lump on his tendon," said Biarritz doctor Jean-Louis Rebeyrol.
"This is what triggered the operation. We cannot foresee a return to competition for at least six months."
France coach Bernard Laporte admits he is concerned by the news ahead of Les Bleus' RBS 6 Nations opener against Ireland at the Stade de France on February 14.
He said: "Thion's injury is a bad blow for him, his club and the French national team," Laporte told L'Equipe.
"Jerome had a great World Cup, he imposed himself on the international game and has become an important member of the national team.
"It is obvious that the second row will be one of our major problems. Four of our players, who were at the World Cup, are injured.
"This is a delicate situation but I also think some other players could break through. We will study that situation very carefully."