The man, believed to be in his 60s, was rushed to hospital after being given CPR on the scene at the No. Eighteen sauna, at Albert Place, on Leith Walk, but later died in hospital.
It is understood there had been a disturbance at the sauna at around 12.30pm yesterday, although it was not clear whether this was connected to the man’s death.
Police closed off the sauna and the surrounding area for a detailed investigation.
A sign on the sauna’s door said the business would be closed until further notice, and listed a telephone number to contact for local CID.
Last night officers secured the building and fitted a new lock. They were understood to be scouring CCTV from nearby businesses for any clues to the events that led up to the incident.
It is not known exactly what happened, but neighbours reported a disturbance at around lunchtime and said that shortly afterwards they had witnessed the man being rushed outside and given CPR at the back of the building.
Stuart Little, who works at Priscilla’s Bar, next door to the sauna, said a large number of police and CID had been on the street from early afternoon.
He said: “We are not sure exactly what happened, but the police have been asking staff to keep an eye out for suspicious people coming into the pub and they’ve checked our CCTV for people who were coming and going at the sauna.
“Our CCTV covers right up Leith Walk. The place is a gay-friendly sauna and there isn’t usually any bother, often people who’ve been to the sauna will come in here for a drink.
“There were loads of CID and forensics around the place yesterday.”
James Fraser, who lives in the flats at the back of the building, said he saw a lot of commotion at around 1.30pm.
He said: “I saw two police and about four ambulance guys bring the guy out the back to try and resuscitate him.
“They gave him CPR for a while, but it didn’t look good and he seemed to not be responding. I heard the guy later died in hospital.”
On it’s website the No. Eighteen Sauna describes itself as “Edinburgh’s busiest gay sauna” and says visitors “will get a very friendly welcome from the staff and customers alike”.
The sauna is open until 10pm Monday to Thursday, and 11pm on Friday, Saturday and Sunday.
A police spokeswoman confirmed that they were investigating the man’s death.
She said: “Police are investigating following the sudden death of a man at an address in Albert Place, Leith, on Tuesday, September 13. Enquiries are ongoing to establish the circumstances surrounding his death.”
Anyone with information about the incident should contact Lothian and Borders Police on 0131 311 3131.