“Peter Madsen tried to escape,” a Copenhagen police official told AFP.
Police confirmed on Twitter that Madsen had been “arrested and removed from the scene” after being surrounded by police officers, with unconfirmed reports he had threatened them with an explosive device.
Danish tabloid BT reported Madsen had taken a hostage and threatened prison staff with a pistol-like object to force his way out of the facility.
It quoted witnesses who said he managed to drive away in a white van before police stopped him.
Photos from the scene showed Madsen sitting on the grass by a leafy wall next to a road a few hundreds metres from the prison, with two police officers lying prone on the ground pointing their weapons at him.
Madsen, a 49-year-old submarine enthusiast, was convicted in April 2018 of murdering journalist Kim Wall as she interviewed him on board his submarine in August 2017.
In a documentary that aired in September, he confessed for the first time to the killing, after having insisted during the trial that her death was an accident.
“There is only one who is guilty, and that is me,” Madsen said in the documentary.