The 21-year-old victim was walking in Dover Street, Glasgow, at about 9.15pm on Saturday when the three men attacked him.
Police said one of the men stabbed the victim in the face and they then ran off towards Argyll Street.
The victim was taken to the Queen Elizabeth University Hospital for treatment and was later released.
The three men police are hunting are said to be Asian and in their mid twenties.
One is about 5ft 6ins with short dark hair, facial stubble and slim. He was wearing a grey baseball top with black sleeves and buttons down the middle.
The second man is 6ft with short black hair, clean shaven and was wearing a red jumper or jacket.
The third man is 5ft 10ins with receding short black hair and was wearing a cream long-sleeved top during the attack.
Detective constable Graham Morrison said: “This would appear to be a totally unprovoked attack which has resulted in a young man sustaining serious facial injuries.
“We are carrying out door-to-door enquiries and viewing CCTV in an attempt to identify the men responsible for this vicious attack.
“In the meantime, I urge anyone who either witnessed the incident or anyone who remembers seeing the three Asian men hanging around the area either prior to 9.15pm on Saturday or running off afterwards to contact police immediately.
“It is believed that they may have got into a car that was parked nearby.”