The 34-year-old Italy international took an early knock in Sunday's 1-0 Serie A victory over Udinese and limped off the Juventus Stadium pitch after only 13 minutes.
Medical tests conducted in Turin on Monday have since revealed "a second-degree lesion to the collateral medial ligament in his right knee", according to an official club statement.
The reigning league champions, who lead the current table by three points from Roma, did not offer a prognosis for the playmaker's recovery but he can expect to miss 40 days of action.
Juve must face Bologna, Sassuolo and Atalanta in the league before the winter break, with Pirlo also unavailable for a difficult Champions League Group B meeting with Galatasaray in Istanbul.
The former Inter Milan and AC Milan player joined the Bianconeri on a free transfer in 2011 and has won back-to-back Serie A titles under the management of Antonio Conte.