The alert was raised after James Stewart, aged 24, was reported missing from an address in Glasgow on Friday afternoon.
He disappeared following home leave from Castle Huntly open prison, near Dundee.
It is thought he has connections in the Glasgow area.
Police believe Stewart does not present a threat to members of the public.
He is described as 6ft tall, of average build with short brown hair, brown eyes and a small scar on his left eyebrow, and wearing black-framed glasses.
The 15th-century Castle Huntly is Scotland’s only open prison.
Most inmates are low-risk, serving short sentences of up to two years, although some are long-sentence prisoners nearing the end of their term.
Anyone sighting the prisoner should contact Police Scotland on 101.
Anyone wishing to provide information anonymously can do so through the charity Crimestoppers on 0800 555 111.