Bovo got hurt in last week's 1-1 draw at Genoa and will be sidelined for six weeks.
A statement from Torino read: "Cesare Bovo underwent a menisectomy in his right knee.
"The estimated time of recovery will be approximately 45 days."
The 30-year-old has made seven league appearances for the Turin outfit, who is seventh in Serie A.
Torino visit Udinese this weekend before ending the year at home to Chievo.