The men were attacked at Barkly Square in Brunswick on Monday morning.

Police have been told one victim, a 60-year-old Brunswick man, was standing in a Woolworth's checkout queue when he heard yelling behind him.

When he turned around, the customer was stabbed in the upper body by a man in the queue.

The alleged attacker, a 20-year-old Brunswick man, ran from the store and a security guard who heard the yelling confronted him and was also stabbed.

The man then entered an electronics store and was tasered after police tried to negotiate with him.

He is currently in hospital with self-inflicted injuries, while both victims were also taken to hospital in a stable condition with non-life-threatening injuries.

Police say they are not searching for anyone else over the incident and there is no threat to the community.

Investigators at the scene said it was a "completely unprovoked" attack.

In a statement, Woolworth's thanked its staff for responding to the customer's safety.

"There is no place for violence like this anywhere in our community," it said.

"The store will remain closed until further notice while we focus on supporting our team and assisting Victoria Police with its investigation."

Witness Suzanne said she was petrified as nearby shopkeepers locked themselves inside during the incident.

Barkly Square was closed for the remainder of the day but is expected to reopen on Tuesday morning.

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Australian Associated Press