TEHRAN, Young Journalists Club (YJC) - NSW Police received reports of the incident at the intersection of Anderson Street and Victoria Avenue just after 3:45pm on Saturday.
A 22-year-old woman was airlifted to Royal North Shore Hospital with serious injuries.
Four others, including a 16-month-old girl, were taken to hospital and are being treated for minor injuries.
Police said the incident was not a deliberate act and they believe the 50-year-old male driver may have suffered a medical episode before mounting the footpath.
"We've been talking to the driver," Inspector Kylie Smith said.
"It's a motor vehicle accident where it appears the driver has had some sort of medical episode."
Evita Barboza, who was at the scene, said her first thoughts were of the recent attacks in Spain.
"My son saw the whole thing, lucky he didn't get hit," she said.
"I heard the helicopter and all these things and I didn't know what was happening.
"It's really scary, I'm Spanish and because of what happened in Barcelona yesterday and all the things that are going on in the world."
A worker at a nearby store, who asked to remain anonymous, said the car mounted the footpath before hitting pedestrians.
"It went up the walkway then went past the shop, next to our shop and I think it crashed with a pram and a pair of grandparents," they said.
Officers from North Shore Local Area Command have established a crime scene and police from the Metropolitan Crash Investigation Unit will be investigating.