The Brazil international suffered the setback during the Ligue 1 champions' 1-1 draw with table-toppers Monaco on Sunday and was forced off in the 16th minute.
Blanc admitted that although he could not put an exact time on how long his captain would be out for, the injury is a muscle and tendon problem.
He said: "Thiago has undergone tests that have confirmed a problem with the muscle and the tendons.
"So it is not just muscular and I think he will be out for a certain period. I am not a doctor, I can't be more precise."
Early reports claim that the 29-year-old could be out of action for up to six weeks, a spell that would see him miss important league matches against Marseille and Saint-Etienne.
The former Milan star could also be absent for the UEFA Champions League ties against Benfica and Anderlecht as they look to build on their win over Olympiacos in their opening game of the competition.
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