The 16-year-old victim is still in hospital with a chest wound after the attack in Gilmerton yesterday afternoon.
He was attacked at about 5.10pm and found lying on the pavement outside the Aldi supermarket on Gilmerton Road.
A police spokeswoman said: “Police in Edinburgh are investigating following an attempted murder in the Gilmerton area.
“A 16-year-old boy suffered serious injuries to his chest and was taken to the Edinburgh Royal Infirmary by the Scottish Ambulance Service where he remains receiving treatment.
“Inquiries are ongoing and officers are currently following a positive line of enquiry.”
The attack happened in front of horrified shoppers.
Eye-witness William Hill told the Evening News: “Everyone rushed to the boy and I think one woman was an off duty nurse. She was screaming for bandages and scissors.
“It was pandemonium. The youth was just lying on the pavement and had a stab wound on his side fighting for his life. There was a lot of blood and he seemed unconscious.”
A shocked Mr Hill went searching for assistance to aid the man before emergency services arrived near the Aldi store on Gilmerton Road.
“I was knocking on doors trying to find some help,” he said.
“It was absolutely horrifying and not something you would expect to see on a busy street in broad daylight.
“Police arrived first and they didn’t have any first aid boxes in the cars which I couldn’t believe. In the end there were about five police cars and two ambulances. I just hope the boy survives.”
Anyone with information can contact Gayfield CID via 101, quoting incident number 2957 of 14 April.
Alternatively Crimestoppers can be contacted anonymously on 0800 555 111.
Sign up to our newsletter: enter your email in the box at the top of this article to get daily updates straight to your inbox.