Police firearms officers responded to reports of a man with a bladed weapon in the Calders area of the city at 08:25.
The two injured people have been taken to the Royal Infirmary of Edinburgh for treatment and police say there is not believed to be any wider risk to the public. The suspect is thought to be holed up in an 11th-floor flat.
A Police Scotland statement said the incident was not being treated as terror-related.
Two local men, who didn't want to be named, said they saw the suspect armed with two blood-stained knives outside a shop shortly after the incident began.
"I got out of my car and the guy came up to me with his hands behind his back. He said, can I speak to you," one man told the BBC.
"He had the two knives behind his back, covered in blood."
The man said an onlooker handed him a spirit level which he then used to confront the suspect.
"He handed me the spirit level and we just started going for it," the man said.
"He started going towards the school so I was just trying to chase him back. He's coming towards me the whole time."
"The police were there but they said they weren't allowed to get out of their car because it was a firearms incident.
"He walked away up to the flats."
Firearms officers are routinely deployed to knife incidents and were seen going into the block of flats.
Paramedics wearing helmets and body armour were also in attendance.
The man suspected of being involved in the incident later appeared at the window of an 11th floor flat in the multi-storey block, looking down at the crowd below.
Members of the public were seen shouting at him and the police extended their cordon to move them further back.
At the scene, people from other flats in the block could be seen at their windows.
Pictures from the scene of the incident show at least six police vehicles outside Cobbinshaw House, a tower block of flats, as well as armed police officers.
Footage which has been circulating on social media shows a man walking in the area holding two large knives, as well as a shop which had been damaged.
William Ramsay, who lives in the area in the west of the city, said he believed the man with the weapons had entered the stairwell of his building.
"He smashed the local shop, possibly stabbed two people unconfirmed," he told the Press Association.
"Armed police, dogs been here for about two hours."
What a complete faggot.
The two injured people have been taken to the Royal Infirmary of Edinburgh for treatment and police say there is not believed to be any wider risk to the public. The suspect is thought to be holed up in an 11th-floor flat.
A Police Scotland statement said the incident was not being treated as terror-related.
Two local men, who didn't want to be named, said they saw the suspect armed with two blood-stained knives outside a shop shortly after the incident began.
"I got out of my car and the guy came up to me with his hands behind his back. He said, can I speak to you," one man told the BBC.
"He had the two knives behind his back, covered in blood."
The man said an onlooker handed him a spirit level which he then used to confront the suspect.
"He handed me the spirit level and we just started going for it," the man said.
"He started going towards the school so I was just trying to chase him back. He's coming towards me the whole time."
"The police were there but they said they weren't allowed to get out of their car because it was a firearms incident.
"He walked away up to the flats."
Firearms officers are routinely deployed to knife incidents and were seen going into the block of flats.
Paramedics wearing helmets and body armour were also in attendance.
The man suspected of being involved in the incident later appeared at the window of an 11th floor flat in the multi-storey block, looking down at the crowd below.
Members of the public were seen shouting at him and the police extended their cordon to move them further back.
At the scene, people from other flats in the block could be seen at their windows.
Pictures from the scene of the incident show at least six police vehicles outside Cobbinshaw House, a tower block of flats, as well as armed police officers.
Footage which has been circulating on social media shows a man walking in the area holding two large knives, as well as a shop which had been damaged.
William Ramsay, who lives in the area in the west of the city, said he believed the man with the weapons had entered the stairwell of his building.
"He smashed the local shop, possibly stabbed two people unconfirmed," he told the Press Association.
"Armed police, dogs been here for about two hours."
What a complete faggot.
