The woman was attacked about 8:40 p.m. while visiting someone on the fourth floor, said Investigator Brandon Beckman.
The man was armed with a steak knife, but fled when another woman entered the restroom.
Photos and video of the suspect have been posted on news Web sites the last several days, but there have been no major leads as of Saturday night, Investigator Beckman said.
Police also believe the man could be linked to a waiting room theft on the same floor of the hospital last week, Investigator Beckman said.
The man is described as a black male, standing about 5-feet-8-inches tall, weighing about 160 pounds with a bald head.
Anyone with information can contact the Richmond County Sheriffs Office Crime Investigation Division at (706) 821-1020.