Police say the three separate violent incidents in inner-Melbourne were random attacks and not thought to be terror-related.
Investigators are probing whether a fourth stabbing is also linked.
A Melbourne man, 24, was attacked outside a burger shop at King Street in the CBD about 10pm on Saturday after the alleged offender lunged and stabbed him from behind.
He was taken to hospital with a leg injury.
About an hour later, 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 after initially suffering life-threatening injuries and her partner, a Glen Waverley man, had a serious laceration to his arm.
At about 12.30am on Sunday, a 31-year-old English national was attacked on Acland Street in St Kilda and taken to hospital with non-life threatening leg injuries.
Police believe an earlier stabbing of a 28-year-old Mount Waverley man at City Road in the CBD, at 9.20pm on Saturday, may have been the first incident in the series of attacks but are yet to find the evidence linking it.
Detective Senior Sergeant Andrew Eyries said it was 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," Sgt Eyries said.
The weapons used were believed to be knives found in any kitchen and were easily accessible, he said.
The Melton man, 31, was in custody assisting police with their inquiries.
He was showing signs of mental health or drug and alcohol issues and would need 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.
Sgt 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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