The crash was the first of two serious collisions involving pedestrians in San Francisco on Wednesday, according to police.
Another later in the day in the Bayview District left an elderly woman with life-threatening injuries.
In the earlier incident, a woman had been crossing the street at Waller and Cole streets at about 8 a.m. when she was struck by a black Toyota Prius, police spokesman Sgt. Troy Dangerfield said.
"The Prius never stopped, and fled the scene," Dangerfield said.
The woman died at the hospital at 1:50 p.m. Wednesday, according to Dangerfield.
She was identified today by the medical examiner's office as Joyce Lau.
Police later tracked down the driver of the Prius, Iddo Avital, 26, at a home in San Francisco, and arrested him, Dangerfield said. The vehicle was also recovered.
At about 5 p.m. Wednesday, another woman -- also around 70 years of age -- was crossing Bayshore Boulevard near Bacon Street when a vehicle turning onto Bayshore hit her, Dangerfield said.
The woman was hospitalized with life-threatening injuries. Dangerfield did not have an update on her condition this morning.
According to Dangerfield, the woman had been crossing on a green light.
The driver remained at the scene and has not been arrested, Dangerfield said. There was no indication alcohol was involved in the crash, and an investigation is ongoing, he said.