Two of the victims are said by police to be in a critical condition, while the other two were described as stable.
Police are scouring the Edmonton area for the single male attacker, who is described as black, about 6ft 3ins, of skinny build and wearing dark clothing, possibly a hooded top.
All four victims had been alone at the time and attacked from behind without warning.
:: First attack A 45-year-old woman is in hospital in a critical condition after being stabbed in the back in Aberdeen Road at about 7pm last night.
:: Second attack The victim was stabbed four hours later in Park Avenue.
He was taken to hospital for treatment, but his condition is not life threatening.
:: Third attack Shortly before 4am this morning police received reports of a man stabbed at Seven Sisters tube station, but investigators believe he may have sustained his injuries in Silver Street, Edmonton.
The 23-year-old remains in hospital in a critical condition.
:: Fourth attack The most recent stabbing place just before 10am this morning in Brettenham Road in N18.
His injuries are potentially life-changing.
Acting Detective Chief Inspector Stuart Smillie said police were doing everything they could to “to apprehend the suspect behind these cowardly and senseless attacks”.
He said: “We believe the culprit knows Edmonton and may well be from the area.
“The motive for the stabbing appears to be solely to inflict harm.”
He added: “The four victims are all from different backgrounds and appear to have been selected at random due to them being alone and vulnerable. There is nothing to suggest this incident is terror related.
“We are working on the hypothesis that the single male suspect is acting alone and mental health issues may be a factor.
“All of the people he has targeted have been walking alone and he has approached from behind without warning.”
A man was arrested on suspicion of grievous bodily harm shortly before 11am in Edmonton and inquiries continue to establish if he is the suspected attacker.
Dervish Husseyin, 60, was at his friend’s house on Aberdeen Road when the first stabbing took place.
“I seen the woman lying down, face down,” he said, adding: “She said they had beaten her up.”
Mr Husseyin said the woman had “blood on her back” but did not seem to realise she had been stabbed.”She said she only went out for a walk on her own,” he said.
Mr Husseyin said a man who said he witnessed the attack described seeing two black men.
Natasha Cameron, 45, lives on Aberdeen Road and was walking home from work at a nearby casino after 10pm.
She said she saw officers on her road who told her there had been a stabbing but she was unaware of the later attacks.
“I was ‘oh my God this is the road I live on’,” she said.
Ms Cameron added: “I’m scared now because I always walk here from work home.
“Now I’m definitely taking the bus.”