X-rays were negative, the team said.
"We hope that he can recover quickly," coach Jason Kidd said. "He's young. We'll see how he feels tomorrow."
Williams landed on Suns center Miles Plumlee's left foot and immediately went down in pain. He eventually was helped to his feet and hopped toward the tunnel at U.S. Airways Center, unable to put any weight on the ankle.
"All my weight was on [the ankle]," Williams said of how he sustained the injury. "It's frustrating. No words can describe it. Sick of getting injured, sick of being hurt. I just want to be healthy and help my team."
Williams tweaked the same ankle Wednesday against the Kings in Sacramento when he backed into teammate Andray Blatche late in the second quarter. He remained in the game.
Williams has been slowly recovering from a sprained right ankle and a bone bruise he suffered during an offseason workout in Utah. The 29-year-old went into Friday night's game averaging 11.1 points and 7.4 assists per game. His player efficiency rating (13.71) is below the league average (15.00).
Although Williams has said he's been feeling more like his old self lately, he's looked uncomfortable in the team's new offensive system under rookie coach Kidd.
Shaun Livingston replaced Williams against the Suns.
The Associated Press contributed to this report.