In an unusual move in Germany, a photograph of the man, named as Wolfgang Dorf, was released on Sunday as police in Mainkofen launched their appeal for information.
A statement said he absconded from a hospital while receiving court-prescribed treatment there.
“Mr. Dorf was sentenced to a long period of incarceration for, among other things, sexual crimes,” the statement said.
A police spokesman told The Local that Dorf had been in prison for around 20 years. It is not thought he attacked children.
In Germany sentences are generally limited to 15 years maximum even for murder, with people only held for longer if they are considered to be dangerous.
"We are using all facilities available to us," the spokesman said. "That includes following up any potential contact he might make to others such as family."
He said Dorf's picture was being sent to police forces around the country.
Dorf is described as 1.78 metres tall, lean, with dark blonde hair, a distinctively receded hairline, and glasses.
He could be in the company of a man and two women, all around 25 years old, who were also at the hospital and fled with Dorf. They are not thought to pose a risk.
The Süddeutsche Zeitung said on Monday that Dorf, who is 46, was not being monitored when he simply left the hospital grounds.
Anyone who sees him should call the police on 09421 8680.