The woman was responding to treatment at a hospital with her family by her side, Hayes said.
He did not know her condition or injuries, but "at least there's a fighting chance" she will survive, he said.
The SUV plunged into 15 to 17 feet of water. Divers needed about 20 minutes to reach it, he said.
However, the windows were rolled up, so there may have been a pocket of air inside, he said.
Hayes earlier said a body was pulled from the car. He indicated the woman was limp and unconscious when divers broke into the vehicle and found her. Hayes said she was found to have a pulse although he did not know whether she was breathing.
The river channel, part of a flood control system, was clouded with silt and runoff. A dozen divers working in teams hunted for the car in zero visibility and a strong current, Hayes said.
Authorities at first thought there might be as many as two other people in the car after divers working by touch discovered an infant car seat in the vehicle, Hayes said.
However, the woman's family later confirmed she was alone, he said.
The bridge is an area where freeway traffic slows and makes a sharp turn, and other vehicles have plunged off it in the past, Hayes said.