A man found carrying a bag of knives after he allegedly went on an unprovoked stabbing spree is set to face court on more than a dozen assault charges.

Police say the four separate violent incidents in inner Melbourne over three hours on Saturday and Sunday were random attacks and not terror-related.

A 28-year-old Mount Waverley man was stabbed on City Road in Southbank, at 9.20pm on Saturday.

He was taken to hospital with non-life threatening injuries to his leg and torso.

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About 40 minutes later, a 24-year-old Melbourne man was attacked outside a burger shop at King Street in the CBD after the alleged offender lunged and stabbed him from behind.

He was taken to hospital with a leg injury.

About 11pm, a man and a woman, both 31, were stabbed while walking along Dandenong Road in St Kilda East.

The St Kilda East woman is in a serious but stable condition and her partner, a Glen Waverley man, had a serious laceration to his arm.

A 31-year-old English national was attacked on Acland Street in St Kilda at about 12.30am on Sunday, and taken to hospital with non-life threatening leg injuries.

Police have charged a 31-year-old Melton man with 14 counts of assault causing injury and one count of possessing a controlled weapon.

He has been remanded in custody and is expected to face the Melbourne Magistrates Court on Monday.

Detective Senior Sergeant Andrew Eyries alleged the man set upon people who wouldn’t have known they were about to be attacked.

“The victims … are people that were just going about their own business and have been cowardly attacked,” he said.

The alleged offender was spotted by a protective services officer and arrested at Balaclava Station in South Yarra carrying a bag containing multiple knives.

“It’s quite possible that different edge weapons were used at each individual scene and that’s consistent with the varying injuries and severity of the injuries,” Eyries said.

The weapons used were believed to be knives found in any kitchen and were easily accessible, he said.

The man had shown signs of mental health and drug and alcohol issues and needed to be medically assessed before being interviewed, Sgt Eyries said.

Officers stressed there was no further danger to the public and they were not looking for anyone else.

Eyries urged the public to “have faith in police” despite the alleged offender being on the loose for hours across the public transport network.

“Although there are (four) linked incidents with five victims, I would say that it was the police response that resulted in disrupting any further offending,” he said.

Eyries said the alleged offender was wearing a very distinctive lime-green hooded windcheater and all dark cargo-style pants, urging anyone who saw the attacks to contact Crime Stoppers.

Police are particularly keen to speak to a woman who may have seen the Southbank stabbing but left before speaking to officers.

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-AAP