Both players were hurt Saturday in a 76-71 victory over New York that left Charlotte at 19-26, one win ahead of Brooklyn in the eighth and final Eastern Conference playoff position.
Williams was diagnosed with concussion and a broken nose while Biyombo, a center from the Democratic Republic of Congo, suffered a bruised bone in his right knee.
Williams, averaging 6.5 points and 4.5 rebounds over 43 games this season, cannot practise or play in games until he passes NBA concussion protocol tests.
Biyombo, who will be re-evaluated in about 10 days, is averaging 4.6 points and 6.2 rebounds over 38 games. The 22-year-old African big man is in his fourth NBA season after a stint with Spain's Fuenlabrada in 2011.