The transport management centre told motorists to avoid King Street due to the operation.
A Sky News reporter and other media reports said the man shouted "shoot me" at police.
The woman was taken out of the Hotel CBD and placed into an ambulance.
The man then ran down a nearby street. The offender has blood on his hands.
"We managed to get a grip along with another guy and we've got a grip of him and restrained him fully", he said.
"We put a plastic crate over him, over his head".
The Irishman paid tribute to the bravery of the public in helping to bring the man under control.
"He stabbed her. He came running through the street". I was like, "Luke, be careful, be careful".
Shane moved to Australia with his mother and father and the rest of the family in 1988.
Walker said the man with the chair, whom he identified as a bank worker, had used the chair "like a lion tamer", trying to turn the man around as he ran through the city streets.
Superintendent Wood lauded the actions of the bystanders who restrained the alleged offender and called them "heroes". He said: "I don't think that is religion in any way from what I know of all the different religions".
- Andrew Denney (@Andrew_Denney) August 13, 2019Some psycho just went around stabbing people in Sydney.
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"We all kind of chased, worked together, but it was Luke who was the real hero".
Police blocked off King, Wynyard and Carrington streets just after 2pm.
"Paul and Luke are extremely respectful, but also have a great sense of justice and civil responsibility", Adam Loster, acting principal at their school St Gabriel's, told the newspaper.
"Our immediate reaction was, right, let's go and help, if he's wielding a knife". They not only saved lives, but they made sure this lunatic will get what's coming to him ... we hope.
"He had a knife".
He added the man had "blood all over him".
But police say the man did not have any known links to terror groups, and that he acted alone.
Paul, a father-of-two who has lived in Sydney for 11 years, said he felt it was his way of giving back to a country which had welcomed him with open arms.
He said that the man "was shouting radical things" but that he did not want to repeat them.
"Information was found on him that would suggest he had some ideologies related to terrorism ... but he has no apparent links to other terrorist organisations", NSW Police Commissioner Mick Fuller told the Morning Herald.
NSW Police gave an evening update on Tuesday's CBD incident, where one woman was stabbed in the back and another woman was found dead in a nearby building.
Mr Wood said: "They are significantly fearless people".
"And I want to acknowledge those people, those members of the public who got involved".