NSW Police said they received reports of a man walking along York Street with a knife around 2pm.
She's been taken to St Vincent's Hospital in a stable condition.
Police arrived on the scene following multiple reports of a stabbing near the corner of King and Clarence Streets.
Members of the public rushed to detain the man, using milk creates and chairs, before he was arrested by police and taken to Day Street Police Station on a stretcher.
Witnesses told AAP a young man armed with a 30-centimetre kitchen knife had been yelling religious statements.
Video footage on Twitter showed a young man running across a city intersection and jumping onto the hood of a auto, waving what appeared to be a knife.
Police have reported one woman has been stabbed and a man has been arrested.
While the motive of the attack is not yet known, the man has been arrested, police said.
The alleged attacker was filmed climbing a moving Mercedes-Benz, before screaming "shoot me" repeatedly as people tried to bring him under control.
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Several men are seen circling the alleged knifeman, trying to coral him away from others.
Paul O'Shaughnesy's first thought when he saw a blood-soaked man wielding a knife in the centre of Sydney was for the safety of others.
The group then worked together, according to interviews in The Age, to overcome the knife-wielding man. "I want to acknowledge those members of the public who got involved", he said. "More to come." said NSW Police Force on Twitter.
"Those attempts thankfully were unsuccessful", said Supt Gavin Wood of New South Wales Police.
"They were courageous, and and i can only use that word seriously, they were significantly fearless people".
'So insane! A random dude just started stabbing people in the city right outside where we were having lunch, ' @JackHuddo said on Twitter.
NSW Police have set up a series of roadblocks in the area.
"A number of crime scenes have been established and a number of road closures are in place, which is believed to have significant impact on traffic and public transport this afternoon".
A woman's body has been found in a building in central Sydney after a major police operation shut down part of the CBD. "I saw people running so I ran towards him with a few other guys", Jack Huddo said on Facebook.