Grant Redpath from Ormiston Road in Tranent, East Lothian, was last seen around 10am today (Monday) leaving the Royal Infirmary of Edinburgh.
However, the 37-year-old has failed to make contact with anyone since then and concern is now growing for his wellbeing.
Anyone who can assist in locating Grant is asked to come forward.
He is described as white, 6ft 2ins tall with a stocky build and short shaved brown hair. He was last seen wearing jeans, a beige jumper, black puffer jacket and Timberland boots.
Inspector Alan Hogarth said:
Grant left the hospital on Monday morning but gave no indication as to where he was going and has not been in touch with any family or friends.
As such, we are keen to trace him as soon as possible and establish he is safe and well.
Anyone who believes they have seen Grant since 10am on Monday, or who has information that can assist in locating him is asked to contact police immediately.
Those with information can contact Police Scotland on 101.