Madsen was rescued on Friday morning in a navy operation and taken ashore after his homemade 17-metre submarine went down.
Press reports named the Swedish journalist as Kim Wall, 30, who was writing a feature story about the inventor.
The submarine is lying in 7ft of water, but divers have not been able to enter it safely yet, police said.
A search for the missing submarine was launched after Ms Wall's boyfriend raised the alarm.
"Whether the woman was on board the submarine at the time of her disappearance is unclear", police said in a statement.
The Sweden-born freelance journalist studied at the Sorbonne university in Paris, the London School of Economics and at Columbia University in NY, where she graduated with a master's degree in journalism in 2013.
She also received a master's degree in journalism from Columbia University in NY in 2013.
A Danish court today ordered that Madsen be held in pre-trial detention while authorities investigate Wall's disappearance, the Associated Press reported.
Madsen "told us he had technical problems" when asked to explain why the submarine failed to respond to radio contact earlier in the day, Damgaard said.
Peter Madsen was arrested Friday on preliminary manslaughter charges, hours after his 40-ton, almost 18-meter-long (60-foot-long) submarine sank off Denmark's eastern coast.
The statement did not identify the submarine's owner, Peter Madsen, 46, but the Danish inventor's financing of the project through crowdfunding and first launch of the UC3 Nautilus in 2008 made headlines. Denmark's navy says that Madsen's privately built submarine that had been feared missing in Danish waters has been found and the crew is safe.
Its owner Madsen was rescued shortly before, but there was no sign of the Swedish journalist.
Danish police said on Saturday they were preparing to search a sunken submarine owned by Danish inventor Peter Madsen who has been charged with the inadvertent manslaughter of a journalist. The navy says that the 40-ton, almost 18-meter-long (60-foot-long) submarine with at least two people on board had been "found sailing" south of Copenhagen.
They described her as "160cm tall, 56kg, 30 years old, with reddish-brown hair and green eyes".