The attack happened at about 6.30pm on Saturday, in Mark Lane, off The Headrow.
Officers were called after the victim, a 34-year-old man, was found with a knife wound to his left forearm in nearby Dortmund Square.
Police said he was stabbed during an altercation with another man, which started after the offender assaulted a woman who was with the victim.
She was thrown to the ground.
The man's injuries were not life-threatening, though he requires further surgery, and both victims were taken to hospital.
Police have appealed for witnesses to the attack.
The offender has been described as black, aged 20 to 30, about 5ft 11ins tall, of skinny build with black curly hair.
He was wearing a black silky coat and black trousers.
Anyone with information is asked to contact Leeds District CID via 101, quoting crime reference 13180552084 or call the independent charity Crimestoppers anonymously on 0800 555 111.