The 31-year-old announced his season had been cut short and the lengthy lay-off on his Twitter account on Monday.
Clerc, who left the field in the 52nd minute of the 39-17 loss against Clermont, said: "The news is not very good unfortunately.
"The injury will require several months off! Appointment early next season!"
It means Clerc will not be available for the three Test match tour of New Zealand in June, where Les Bleus will also face Auckland in a midweek fixture.
The winger has previously ruptured cruciate ligaments in his other knee almost five years to the day, which also happened in a Top 14 defeat to Clermont.
Clerc's injury means he will also miss Toulouse's last game of the regular season against Grenoble.