Paul Brownlie, a restricted patient at the Rohallion Secure Care Clinic in Perth, went missing from the outing in the city on Wednesday.
The 33-year-old is white, about 5ft 10ins with a stocky build. He has blue eyes, short fair hair and was wearing a navy jacket, white t-shirt, blue jeans and white trainers.
He is believed to be in the Edinburgh area.
Authorities said they are keen to trace him as soon as possible and anyone with information has been asked to contact police.
A Scottish Government statement said: "Although he is not considered to be a high risk of harm, the public are advised not to approach him.
"If anyone sees him, or has any information regarding his whereabouts, they should contact Police Scotland on 101."