Two people inside a high-street shop and a third person outside were stabbed in the western Sydney suburb of Merrylands on Tuesday morning.
One victim, a man aged in his 30s, was declared dead at the scene.
Another man, 22, and a woman, 47, were taken to hospital in critical conditions.
The alleged attacker fled on foot but was arrested in a nearby street.
Forensic police on Tuesday afternoon were seen entering and exiting a Nepalese grocer and a corridor leading to an accounting firm and training qualification organisation.
A knife about 25cm long was used in the stabbings, Superintendent Simon Glasser said.
"The alleged offender is known to police for petty crime and a number of mental health incidents," he told reporters.
"He's not linked to the address he was located, however he is a local to the area."
Early investigations suggested the victims were unrelated to one another, he said.
Police have not formally identified the dead man.
"As far as we're aware at this point there is no relationship between the three victims," Supt Glasser said.
"They were by themselves on Merrylands Road when this has occurred."
The lethal incident would have been "highly confronting" for passers-by before lunch, when lots of people were on the shopping strip near the local train station.
The arrested man is expected to be charged later on Tuesday.
Staff at a restaurant across the road from the scene said they didn't see the attack but expected it would have an impact on trade in the area.
"It's very quiet now ... it's going to affect a lot of our business because normally we have so many people coming for lunch," the manager of the Kabul House Afghan restaurant told AAP.
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