Officers were called to the premises, on Duke Street, at 9.40am on Wednesday following a report of an assault in the area.
A spokesperson for Police Scotland said paramedics were called and one man was taken to hospital for treatment with an injury to his head.
They added: “Police in Edinburgh were called to the Duke Street area at around 9.40am on Wednesday March, 20 following a report of an assault within a premises.
“A 41-year-old man has been taken to hospital by the Scottish Ambulance Service with serious injuries.
“Two men, aged 35 and 31, have been arrested in connection with the incident and inquiries remain ongoing.”
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