The unidentified man had also tried unsuccessfully to stab other people, police said, in an incident that brought the central business district in Australia’s largest city to a standstill in the early afternoon.
“We have a female person with a stab wound to the back currently being treated by paramedics and is en route to a Sydney hospital,” Police Superintendent Gavin Wood told reporters in Sydney.
He said the woman’s injuries were not life-threatening. He also said the attack appeared to be unprovoked but police were keeping an open mind.
Police were also investigating whether the body of a woman found inside an apartment near where the stabbing took place was linked to the incident.
Video images on Twitter showed a young man running across a city intersection and jumping onto the hood of a car, waving what appeared to be a long-bladed knife.
The man, who was yelling, fell to the ground when the car moved and was confronted by a person holding a chair, the video showed. It was unclear what the man was calling out.
Other footage showed the man pinned to the ground by several people holding two chairs and a milk crate on top of him.