The alleged attack, which left two other people in hospital in critical condition, happened in the western Sydney suburb of Merrylands on Tuesday morning.
A 25-year-old man stabbed two people inside a high-street shop and the third outside the venue, police have alleged.
The alleged attacker fled on foot but was arrested in a nearby street soon after, and was later charged with murder along with two counts of causing grievous bodily harm with intent to murder.
He was refused bail and will appear in Parramatta Local Court on Wednesday.
A 38-year-old man was declared dead at the scene, while a 47-year-old woman and a 21-year-old man remain in hospital.
On Tuesday, forensic police 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 (where) he was located, however he is a local to the area."
Police did not find a relationship between the victims and treated the investigation as if the attacks were random.
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, Supt Glasser said.
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.
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