A group of five men and women were walking on Middle Meadow Walk from Forest Road at about 05:15 on Tuesday.
One of the group was approached from behind by an unknown man who assaulted him.
The suspect was described as white, 25 to 30, with a medium to stocky build and shaved head.
He was wearing a light tweed-style jacket with dark chino trousers.
The man was last seen making off towards Melville Drive.
Det Con Kevin Tait said: "This was a seemingly unprovoked attack which caused extensive facial injuries to the victim and we are pursuing all possible lines of inquiry in order to trace the perpetrator.
"Anyone with information which can assist with our investigation, or who may have seen the someone matching the suspect's description around the time of the incident, is asked to get in touch."
A 19-year-old man was left with serious facial injuries after an "unprovoked attack" in the Meadows area of Edinburgh, police have said.