The incident happened in Dugald Drummond Street, near to Greetham Street, at about 7.15pm last night.
The victim, who is in his 20s, was injured following an argument involving two people.
His injuries are not life-threatening, police have said.
A spokesman for Hampshire Constabulary said: ‘The person with the knife was described as a teenage boy, white, slim, and wearing a grey tracksuit with black stripes down the side. He may have also sustained injuries during this incident but this is not confirmed.
‘Officers would like to hear from anyone who witnessed this take place.
‘We know there were at least two vehicles that drove past during the incident. One was a Müller milk delivery lorry, and the other was a silver/ grey estate style vehicle.
‘The driver of the silver/grey vehicle got out of the driver’s seat and spoke to the injured man.
‘We are particularly interested in identifying and speaking with this driver, and anyone else who witnessed the incident or has any information.’
Anyone with information is asked to contact police on 101, quoting 44210224141.
Alternatively, you can contact the independent charity Crimestoppers 100 per cent anonymously on 0800 555 111, or via their anonymous online form at crimestoppers-uk.org.