James Casey failed to return to HMP Castle Huntly near Dundee after day release and was reported missing at 21:00 on Thursday.
He was jailed for life in 1990 for the murder of a social club manager during a robbery. He was released in 2002 but jailed again for armed robbery.
Officers believe the 50-year-old may have travelled to Inverness.
Casey was ordered to serve at least 11 years after murdering the club manager in Invergordon in 1990.
He was released on licence in 2002 but just weeks later carried out an armed robbery at a post office in West Lothian. He was sentenced to a further 14 years.
In 2011, he appealed his murder conviction, blaming an accomplice, but the appeal failed.
He is described as 5ft 8in tall with receding hair and brown eyes. He was last seen wearing a blue coat, a black hooded top, blue jeans and brown walking boots.
Police have warned the public not to approach a convicted murderer who is missing from Scotland's open prison.