The seven-year veteran averaged 14.1 points and 3.6 assists per game through 39 games before sustaining a torn anterior cruciate ligament in his right knee during a Friday loss to Brooklyn.
The Hawks said a magnetic resonance imaging exam revealed the tear after an initial diagnosis of a ligament sprain.
Williams will have surgery at a date to be determined following a period of rest, General Manager Danny Ferry said.
"We are extremely disappointed for Lou and our thoughts and support will be with him during his recovery," he said. "He has been a complete professional in every sense of the word and know that approach, along with his work ethic, will serve him well in his rehabilitation."