New South Wales Police Superintendent Gavin Wood told the media that the incident began at around 2 p.m. when the suspect produced a knife and as a result, the woman was stabbed in the back, reports Efe news.
"There has been, subsequent to that stabbing, a number of attempted stabbings by the same offender," he said, adding that the suspect was in custody.
"No other person was complicit at this stage," Wood said, adding that there were no other injuries.
The injured woman has been taken to the Sydney Hospital and a police statement said she was in a stable condition.
Several videos shared on Twitter by witnesses appeared to show civil and members of Fire and Rescue NSW pinning the man down on the pavement using chairs and a milk crate over his head, forcefully restraining him until police arrived.
Wood called those who detained the suspect before police got to the scene "heroes".
"These people, these members of the public going about their day-to-day business, have jumped into a situation which was extremely dangerous, extremely hostile, and they have brought a person who we will be alleging stabbed a person for no specific reason into custody and allowed us to do our job," he said.
( With inputs from IANS )