The 27-year-old Italy international was forced out of the 4-0 victory after just 21 minutes when he took a knock from a challenge with defender Stefan Radu.
Medical tests at Turin's Fornaca Clinic have subsequently revealed a first-second degree tear of the medial collateral ligament of his right knee.
A statement published on juventus.com confirmed the club's second vice-captain will be sidelined for a period of between 30 and 35 days - ruling him out of Serie A games against Sampdoria, Lazio and Inter Milan.
Marchisio is also expected to miss the opening group-stage game of Juve's Champions League campaign, with the opening round scheduled for September 17-18.
The 39-time Italy cap will also miss World Cup qualifying games against Bulgaria and the Czech Republic in early September.