It was the second such deadly incident involving a vehicle driven by a Palestinian in three months, prompting Israeli Prime Minister Benjamin Netanyahu to immediately order an increase in police presence across the city.
The driver, identified as a 21-year-old Palestinian from the east Jerusalem neighbourhood of Silwan, was shot and wounded as he tried to flee the scene, police spokeswoman Luba Samri said. His condition was described as moderate-to-serious.
Police described the incident as a "hit-and-run terror attack" -- the term for a deliberate attack with a vehicle.
Nine people were hurt, among them a three-month-old baby girl who later died of her injuries, a spokeswoman for Hadassah hospital told AFP.
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Police and medics said that the driver tried to run off after the car hit the pedestrians and came to a stop.
"The driver apparently tried to flee on foot and was shot and wounded by a policeman," Samri said.
"Initial indications suggest this is a hit-and-run terror attack."
During the most recent incident in August, which took place in the same area, a Palestinian man rammed a bus with an excavator, killing one Israeli and injuring five. The driver was shot dead by police.
In today's incident, eyewitness who had just got off the train said the car ploughed into the pedestrians at great speed.
"We saw a car coming from the north at full speed," said Eli Dayan who was standing on the pavement with his son when the car struck.
Aside from the baby who was killed, two other people were seriously hurt, while two suffered moderate wounds and the rest had light injuries, medics said.
At the scene, a silver car with a badly-dented front stood on the pavement and two stationary trains at the nearby tram station, an AFP correspondent said.