The news means the Uruguay striker will miss the crunch top-of-the-table clash at Monaco on 9 February.
It also means he could miss PSG's UEFA Champions League last 16 first leg clash at Bayer Leverkusen on 18 February.
He will also miss the French Coupe de la Ligue semi-final at Nantes on Tuesday, as well as the Ligue 1 reception of lowly Valenciennes on 14 February, which is also his 27th birthday.
Cavani had to come off in the 76th minute of PSG's 2-0 win over Bordeaux after feeling his hamstring.
El Matador, as he is known, has scored 13 goals this season and has struck up an effective partnership with Zlatan Ibrahimovic, the league's top scorer with 18 goals.