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.
The centre-back wrote on his official Instagram account that he would be out for around around six weeks on Tuesday, but Blanc refused to put a date on the influential defender's return though he accepted that his absence could have an impact on PSG.
The former France boss told reporters: "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.
"Obviously it’s a big blow in terms of timing. Whenever you lose a player it is a blow, and when it's a key player it is a very big blow.
"But we must deal with it. We have players available and we need everyone considering our [busy] schedule."
The 29-year-old ex-AC Milan star is set to miss key league games against Olympique de Marseille and Saint-Etienne, while les Parisiens are unlikely to have him available for Champions League ties with Benfica and Anderlecht.