A woman was taken to hospital on Tuesday after she was stabbed in downtown Sydney in what appeared to be an unprovoked attack by a man who has been taken into custody, police said.

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.