The prognosis came after Battier underwent an MRI on Monday morning that revealed the sprain.
Battier injured his knee in the second quarter of Sunday's victory over New York. The 6-foot-8 forward is averaging eight points and 4.7 rebounds.
Houston coach Rick Adelman says Battier's absence will hurt because he is one of the Rockets' best defenders.
The Rockets entered trailing Portland by 4½ games for the eighth playoff spot in the Western Conference.