It happened at about 7.30pm on Ascot Terrace in East End Park.
An 18-year-old man was found to have a serious stab wound to his back.
It had happened during an incident in the street involving a group of young people.
He was taken to hospital for emergency surgery.
His injuries are not considered life threatening.
A large cordon is in place around Ascot Terrace while the scene undergoes forensic examination.
Additional stop and search powers have now been put in place in the surrounding area.
It means anyone in that area may be searched for weapons without police officers having to have their usual grounds to suspect each person searched.
Detective Inspector James Entwistle, of Leeds District CID, said: “We are treating this incident very seriously and are carrying out extensive enquiries to establish the full circumstances and identify those involved.
“The victim has received a very serious stab wound and is continuing to receive treatment in hospital.
“Our enquiries are still at an early stage and we would like to hear from anyone who saw any part of the incident in Ascot Terrace or who has any information that could assist the investigation.
“We appreciate that an incident such as this will cause understandable concern in the community and we are liaising closely with our colleagues on the local neighbourhood policing team who are keeping local community representatives updated and maintaining a visible presence in the area to reassure people.”
The stop and search order covers an area of east Leeds surrounding the A64 York Road encompassing Burmantofts, East End Park, Harehills, Gipton, Halton Moor and Seacroft.
It was put in place at 8.30pm last night for an initial 24 hours.
It will be reviewed later today.
Superintendent Richard Close, of Leeds District, said: “Serious violence involving knives cannot and will not be tolerated and we will continue to take robust action to target those who carry weapons and involve themselves in incidents of this nature.
“We are putting a range of measures in place to deter any further incidents including the use of additional stop and search powers under Section 60.
"This gives officers an increased ability to target those involved in carrying weapons so we can prevent any further offences.
“Officers from the local neighbourhood policing team will also be increasing their patrols and presence in the area.
“We are continuing to take a proactive approach to issues around knife and gang crime alongside our partner agencies, such as last week’s operation focused on the Burmantofts area that saw 22 young men arrested and 65 weapons seized, along with large amounts of drugs and cash.
“I want to reassure people that we remain very firmly committed to keeping our communities safe, and I hope they will be supportive of the approach we are taking.”
Anyone with information is asked to contact Leeds District CID via 101 quoting crime reference 13210303943 or online.
Information can also be given anonymously to the independent charity Crimestoppers on 0800 555 111.