The SUV was traveling on Phan Van Hon Street from District 12 to Hoc Mon District when the accident occurred near Ba Diem Market in Hoc Mon, an hour from the city center.
The male driver, whose identity has yet to be confirmed, first hit a woman on a motorbike knocking her off the vehicle.
He then reversed and hit four other motorbikes behind him, trapping them underneath the car.
The driver then got off, covered the car plate with a cloth, and walked away, leaving his car.
At least four people, including children, were injured and taken to hospital with minor injuries.
The traffic police are investigating.
Last October, also in Saigon, a woman slammed her BMW car into several motorbikes waiting at a traffic light at the Hang Xanh intersection. At least one person died and five people were injured in the accident.
Nguyen Thi Nga, 46, a restaurant owner, was driving under the influence, the police said.
The accident sparked widespread outrage on social media. Nga was arrested and faces a jail sentence of three to 10 years.
Road crashes are a common cause of death in Vietnam, killing almost one person every hour, according to official figures.