The 20-year-old suffered the injury during PSG's 2-1 home win against Nancy in Ligue 1 on Saturday.
Lucas was substituted in the 55th minute and it was initially suspected that he had sustained ligament damage in his left ankle.
However, further medical examinations have revealed that the Brazil international has sprained his ankle and will not need surgery as initially feared.
This two-week injury layoff will see Lucas sit out PSG's games against Saint-Etienne and Montpellier.
PSG are currently four points clear at the top of Ligue 1.