A man was taken to Edinburgh Royal Infirmary after the incident on Elliot Street, off Albert Street, shortly after midday. He is said to be in a stable condition.
The street was closed off for several hours yesterday to allow forensic examinations to be carried out.
The victim is said to be in a stable condition in hospital following the attack yesterday lunchtime.
Connor Craig, who works in a nearby warehouse, said a delivery driver saw the violence as it unfolded.
Mr Craig, 22, said: “I heard two guys started fighting in the middle of the street. They had been arguing and then they started going for each other.”
Albert Street, Dickson Street and Elliot Street were sealed off from about 12.45pm and residents were unable to return to their homes for several hours as forensic teams examined the surrounding streets for evidence.
Crime scene investigators were also seen taking photographs, erecting a forensic tent and peering into nearby wheelie bins.
One man, who lives on Elliot Street, said he had seen spots of blood on the ground following the attack.
Police were unable to confirm rumours that the incident started in a stairwell before spilling out into the street. Officers would not comment on what kind of weapon had been involved.
Residents waiting outside the police cordon said they had been left shocked by the attack. One woman, who did not wish to be named, said: “There have been a lot of incidents around here lately and some drug-related problems.
“I’m not terribly surprised by this. It is not what you would call a quiet area. It’s got quite a transient population with a lot of comings and goings.
“People don’t tend to stay in the way that they used to, with their families.”
She added: “This latest incident has made me quite anxious.”
Another resident, from Dickson Street, described the incident as “troubling”.
She added: “This is terrible but I’m not surprised it has happened because there is quite a bit of bother around here.”
Last night police said they were still to make an arrest or charge anyone.
Yesterday’s attack happened yards from Dickson Street where a 26-year-old man was stabbed to death by his flatmate over unpaid bills in 2012. Maciej Ciania, 34, suffered multiple stab wounds during an attack by his former friend Grzegorz Gamla, who was found guilty of his murder.