The 17-year-old victim was taken to hospital following the alleged attack in Meadowhead, at 3.05pm yesterday.
Two 16-year-old boys have been arrested on suspicion of attempted murder.
The incident happened close to a primary school and not far from a secondary school, both of which have issued statements today in a bid to reassure the community.
In a statement, Liam Colclough, head of school at St Thomas of Canterbury School, said: “Our core priority is the safety of the children in our school.
“We are working closely with the police and there are no ongoing risks in relation to the incident yesterday afternoon.”
Kam Grewal-Joy, headteacher at Meadowhead School, added: “The matter is being dealt with by the police and our thoughts are with the 17-year-old who was injured and his family.
“The incident does not involve any of our students and we await further details from the police.
“Our priority is to ensure that if any of our students are affected by this serious incident, they are offered the support they need.”
The incident has caused alarm in the community and a number of parents dropping their children off at school this morning expressed their concern.
One mum said: “I saw all the flashing lights but I did not know what it was related to.
“It is worrying because it is a bit too close to home.
“You usually hear about incidents like this in the city centre after people have been on nights out not in the middle of the day.”
A 75-year-old grandmother-of-three, who lives close to the scene of the crime, added: “It makes you feel scared to death.
“This is a really nice, quiet area and so you don’t expect it to happen here.
“But at the same time it seems to be happening more and more. You’re always hearing about knife crime. Something needs to be done.”
Temporary Detective Chief Inspector Jamie Henderson said: “Knife crime devastates our communities.
“There is never an acceptable reason for someone to be carrying a knife in Sheffield; we take knife crime and incidents involving knives incredibly seriously.
“I would ask our communities to come forward if they know anyone in their area who is carrying a knife or if they have any information about this particular incident.”
The injured boy remains in hospital today in what police described as a ‘serious but stable condition.’
Police added officers were attending an unrelated incident when they discovered the victim in Chancet Wood Drive with a ‘stab wound to the back.’
Some residents claimed the victim was attacked in a nearby play area in some woods before staggering into the street.
There was evidence that police tape had been up in the play area but the force has not yet confirmed the exact location of the stabbing.
The two arrested boys have been interviewed by police officers and released on bail pending further enquiries.
Anyone with any information should call police on 101, quoting incident number 473 of September 11.