Williams, who is from Aiken, was paralyzed and has no movement from the waist down after he crashed his motorcycle Sunday morning in Marietta, northwest of Atlanta.
Surgery was originally scheduled for Thursday. No reason was given for pushing it back.
Williams, 30, severed his spinal cord after falling on his back and head when he was thrown from his motorcycle, George Peterson said.
Marietta police said in a statement Tuesday morning that Williams was driving at a high rate of speed that was too fast for conditions. Police say he could not negotiate a curve, and the bike slammed into an embankment.
Williams was scheduled to fight Saul “Canelo” Alvarez on Sept. 15 in Las Vegas but that event has been canceled.