Pirlo was injured in the sixth minute of Juve's last-gasp 1-0 win after being on the receiving end of a crunching Andrea Lazzari tackle.
He continued on playing but was withdrawn eight minutes later, with Serie A champions Juve confirming on Monday that he had suffered ligament damage to his right knee.
"Andrea Pirlo, who picked up a knock not long after kick-off in yesterday's fixture between Juventus and Udinese, has undergone medical tests this afternoon," a club statement read.
"The examinations at Turin's Fornaca Clinic have revealed second-grade damage to the medial collateral ligament of his right knee."
Juventus - who have won the last two Serie A titles - top the table by three points after Fernando Llorente's injury-time winner against Udinese.
