Faried is averaging 11.5 points and a team-best 9.2 rebounds.
He was hurt Sunday while driving for a layup against Portland. He said he had never felt such pain and initially feared a more serious injury but vowed to play in the postseason.
The MRI revealed a sprain of what's called the "anterior talofibular" ligament but no fractures, the Nuggets said.
Faried will miss the Nuggets' games at Milwaukee on Monday and against Phoenix on Wednesday.
A win in either game will secure homecourt advantage in the playoffs for the Nuggets, who are an NBA-best 37-3 at home, where they've won 22 straight.