Peter Madsen reportedly took a hostage to break out before he was quickly apprehended near the Herstedvester prison, where he is serving a life sentence for the killing of Kim Wall.
Justice minister Nick Haekkerup called the escape attempt “very serious”.
“It goes without saying that convicted prisoners who have committed the worst possible crimes should not be able to escape from the custody of the authorities,” Mr Haekkerup tweeted.
Police said Madsen appeared to be carrying fake weapons, including a “bogus” explosive belt.
“When we came, he threw away something that looked like a firearm,” said Mogens Lauridsen, operations chief of the suburban Copenhagen police.
Madsen was captured about five minutes after the escape and around 500 metres from the facility, and Mr Lauridsen said that it is not thought that he had an accomplice.
Prison personnel who followed him saw that he had jumped into a passing white van and informed police.
Police officers then found on Madsen “what seems to be a belt with explosives”, Mr Lauridsen said, adding that Madsen was handcuffed, officers stepped back, and he was left on the side of a road while a bomb squad investigated the belt.
Prison head Hanne Hoegh Rasmussen told a news conference that the escape was being investigated and that she could not immediately confirm media reports that Madsen took a female prison psychologist hostage inside the prison.
“No one has been injured physically,” Ms Hoegh Rasmussen said, adding that prison staff were getting psychological support.
In 2018, Madsen was sentenced to life in prison for killing Ms Wall, a 30-year-old reporter from Sweden he lured aboard his homemade submarine in 2017 with the promise of an interview. He dismembered her body and dumped it at sea.
Madsen lost his appeal, shortly after apologising to the victim’s family who were present in the appeals court.