Copenhagen Police have appealed for witnesses who might have been at Refshaleøen at around 19:00 and 22:30 - the times Madsen claims his submarine left and returned.
Madsen, an entrepreneur known as an artist, submarine builder and aerospace engineer, will go before a judge for preliminary questioning on Saturday. Divers had not been able to enter the vessel.
Thirty-year-old freelance journalist Kim Wall was doing a story on the submarine.
Footage aired by Denmark's TV2 shows Mr Madsen getting out of what appeared to be a private boat, giving reporters a thumbs-up sign, saying: "I am fine, but sad because Nautilus went down". The court decision follows Madsen's arrest yesterday on preliminary murder charges.
The journalist had been writing about Mr Madsen and his submarine, which at one stage was the largest privately-made vessel of its kind.
However, when she failed to return home later that day, her anxious boyfriend contacted the authorities, which led to a full-scale search for the submarine in the early hours. "But I guess that was pretty good, because I otherwise still would have been down there". 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.
When asked why he did not respond to radio contact earlier in the day, Madsen told them he had had technical problems, Danish navy spokesman Anders Damgaard told The Associated Press news agency.
It is believed a search will be carried out once the vessel has been towed to port later today.
Madsen describes himself as an "inventrepaneur" on the website for his Copenhagen-based company. "I design and manufacture non-commercial extreme machines, employing teams of volunteering engineers and technicians to challenge the ordinary". "Diving, no matter the method, is very challenging and it*s technically hard to go to beyond where rubber suits and scuba gear can take us".
According to a timeline compiled by police, on Thursday at about 7 p.m. local time (1700 UTC), the sub departed Refshale Island, a former industrial shipyard transformed into a creative hub, for what was supposed to be a short trip.
Two helicopters and three ships scoured the Baltic Sea waters between Copenhagen and the island of Bornholm. It was expected to arrive in the Danish capital by the end of the evening, said a police statement.
He said there had been a problem with a ballast tank that "turned into a major issue".