The Albania international was forced off at half-time in Saturday's 4-0 defeat at Siena and tests conducted on Tuesday confirmed damage to the 28-year-old's lumbar vertebrae.
A statement from the club read: "Cana underwent tests that revealed a fracture of the apophysis transverse in his second and third lumbar vertebrae.
"The player will have to rest for 40 days and the recovery time period is estimated at two months."
The diagnosis means Cana will miss at least 10 Serie A games as well as next month's Europa League tie against Atletico Madrid.
To add to Lazio's woes, Italian midfielders Stefano Mauri and Christian Brocchi are also out injured.
Mauri is sidelined with a thigh problem while Brocchi has yet to recover from a foot injury.