Williams missed 16 games with back problems late in the regular season, then hurt his wrist in Game 2 in Atlanta on Wednesday night.
Mo Evans took Williams' place in the starting lineup.
"It's a part of basketball," Hawks coach Mike Woodson said. "Injuries, you can't control. We've had our fair share this year and fortunately for us, when we've had key guys go down, other guys have stepped in and picked up the slack. Hey, I've got to go with the guys that are in uniform and push them to help us win."
Williams tried to practice Saturday during the Hawks' morning shootaround session. He struggled, and the determination was made to hold him out.
"It didn't loosen up for him," Woodson said.
Williams' status for Game 4 is unknown, though Woodson said he was hopeful that his starting small forward would be available.