Several hundred officers were combing the forest with the help of special forces, helicopters and sniffer dogs on Monday after the man went missing on Sunday.
Police in Oppenau, in south-western Germany, warned local residents to stay at home and not pick up any hitchhikers.
They released a photo of the 31-year-old suspect, who has a bow and arrow, a knife and at least one gun and is known to the police for previous offences, including illegal possession of firearms.
The authorities did not name the suspect, but the Bild tabloid identified him as Yves Rausch, also publishing a photo of him dressed in military fatigues.
Police said they were informed on Sunday morning that a suspicious man was hanging around a hut in the forest.
Four officers sent to the scene said the suspect cooperated at first when approached.
But then he “suddenly and completely unexpectedly” threatened them with a firearm, leaving them “no time to react to the dangerous situation,” police said.
Police are searching for this man. Photo: Oppenau Police/DPA
The man made the officers hand over their weapons before running away, “presumably” taking their firearms with him.
Police described the man as about 170 centimetres (5.6 feet) tall, slim, with glasses, a goatee beard and a bald head.
They said he had spent time in the forest before and had been spotted there as recently as Saturday, so he presumably knew his way around the terrain.
Man spent time in prison
Bild said he lived above a local guest house for three years before being evicted for not paying his rent about a year ago.
He had odd jobs as a rail worker and a golf course caretaker, a former neighbour was cited as saying, describing him as “not an easy person”.
Various weapons and petrol canisters were found in his apartment after he was evicted, as well as a small shooting range in the attic, according to Bild.
The man then reportedly lived in his car by the local swimming pool for a while before moving into the hut at the edge of the forest.
According to Bild, he spent time in prison for shooting his girlfriend with a bow and arrow.
A police spokesman was cited as saying the man was in a state of “psychiatric emergency” and should not be approached.
The police weapons were P2000 semi-automatic pistols that can hold up to 16 bullets each, according to Bild, meaning the man could have an extra 64 shots at his disposal.
By Sebastien Sauges