Kenny Allan, from the Woodburn area of the town, was last seen around 9.50am on Friday within an address in Komarom Place.
He has not been seen since and officers are growing increasingly concerned for his welfare.
Kenny is white, of medium build and around 5ft 8in tall. He has thinning brown hair and brown eyes.
He was last seen wearing a black jacket, blue jeans and brown boots, as well as a watch with a black leather strap and a gold necklace.
Inspector Jocelyn O’Connor, of Dalkeith Police Station, said: “This type of behaviour is considered completely out of character for Kenny and we are eager to trace him as soon as possible.
“I would appeal to Kenny to get in contact with either his family or police to let us know his whereabouts.
“I would also ask anyone who has seen Kenny, or recognises his description, to get in touch with us immediately.”
Those with information can contact Police Scotland on 101.