Abdul Nabi, 30, who was a patient at Midpark Hospital in Dumfries, was reported missing just after 12.30pm on Tuesday.
He is described as being of Asian appearance, with short dark curly hair, about 5ft 7ins and thin.
When last seen, he was wearing a grey t-shirt, blue jeans and trainers.
Police Scotland have urged the public not to approach him if seen, but to contact 999.
Inspector Rory Caldow said “We did have early concerns that he may have been in possession of a knife, however we understand that this is not now the case.
“Mr Nabi is a vulnerable missing man and our concern for the safety of the public centres around the uncertainty of his reaction should he be approached.”