The 21-year-old man is accused killing a 21-year-old woman at a Clarence Street apartment and of stabbing another woman, who is now in a stable condition in hospital, hours later.
The man's attack ended when members of the public tackled the man, wrestling him to the ground and holding him until police arrived.
Authorities say the man was a lone actor and has no known links to terror organisations.
New South Wales Police Commissioner Mick Fuller praised the members of the public who detained the man.
