Officers were called to Leith Walk at about 06:00 following reports about a man with a neck injury.
Detectives said it was believed he sustained the injury sometime between 05:30 and 06:00 in nearby Smith's Place.
He was taken to the Edinburgh Royal Infirmary where his condition was described as serious but stable.
Det Sgt Neil Spowart said: "We're working to ascertain the full circumstances surrounding this man's injury.
"We believe that he was in a business premises on Leith Walk, near the junction with Balfour Street, at around 5am and that the injury was sustained sometime between 5.30am and 6am.
"Anyone who remembers seeing a man in the Smith's Place area around this time, or has any information which may be able to help us establish the cause of his injury, is urged to get in touch."
Police in Edinburgh have appealed for information after a man was found seriously injured in Leith.