The Bianconeri have not indicated how long the 34-year-old could be sidelined, but initial speculation suggests it could be up to a month, ruling him out of the rest of 2013.
A statement on the official club website said: "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.
"The examinations at Turin’s Fornaca Clinic have revealed second-grade damage to the medial collateral ligament of his right knee."
The playmaker was involved in a clash of knees with Udinese midfielder Andrea Lazzari during Antonio Conte's men's 1-0 victory over the Zebrette on Sunday.
Pirlo suffered the knock after only six minutes and attempted to run off the injury before signalling to the bench that he was unable to continue after 15 minutes.
Juventus' win over Udinese stretched their lead in Italy's top flight to three points courtesy of Fernando Llorente's last-minute winner.
The Bianconeri face Bologna on Friday before a crucial Champions League clash against Galatasaray next Wednesday.