Nets coach Jason Kidd said Williams called trainer Tim Walsh on Sunday night saying his ankle had swelled up. He underwent an MRI on Monday morning, which revealed the sprain.
"He wanted to play and we went on the cautious side of him taking the night off," Kidd said. "We'll re-evaluate him tomorrow."
Alan Anderson will start in Williams' place.
Williams has already missed 11 games this season due to a sprained left ankle.
Williams originally sprained his left ankle Nov. 15 in Phoenix. He missed the next two games before returning Nov. 20 in Charlotte, when he sprained it again and missed another nine games as a result.
It is unknown when or how Williams sprained his ankle for a third time. He had told reporters in Oklahoma City on Thursday that he was dealing with an injury, but declined to reveal what it was and said he was going to play through it.
Williams had been averaging 25.0 points on 63 percent shooting in his previous two games, flourishing in a smaller lineup that had him playing off the ball at times.
Last season, Williams was hampered by inflammation in both of his ankles.
Williams, 29, is averaging 13.6 points and 6.9 assists per game for the Nets (12-21) this season. He is shooting 47.6 percent from the field and 41.9 percent from 3-point range.
With Williams out, the Nets decided to recall Tyshawn Taylor from Springfield of the NBDL after assigning him there earlier Monday.
Mike Mazzeo is a regular contributor to ESPNNewYork.com.