The Hawks say Williams will not be with the team for both Monday night's game at New Jersey and Wednesday's game at Indiana.
Williams is averaging 10.9 points and 6.0 rebounds as the starting small forward. He hurt his ankle midway through the first quarter of Saturday's win over the Bulls and did not return.
Atlanta's options at forward include Tracy McGrady and Vladimir Radmanovic. Hawks coach Larry Drew also at times has moved Jason Collins into the lineup at center, pushing Al Horford to power forward and Josh Smith to small forward.