Police would not comment on why charges had been brought before a body had been found.
Madsen, an entrepreneur known as an artist, submarine builder and aerospace engineer, went before a judge on Saturday behind closed doors for preliminary questioning.
A Danish submarine owner has appeared in court over the disappearance of a Swedish female journalist who had been on board his vessel before it sank.
Kim Wall's family said in statement emailed to The Associated Press on Saturday, "It is with great dismay that we received the news that Kim went missing during an assignment in Denmark".
While the UC3 Nautilus was going down, Isbak says "came up again, stayed in the tower until water came into it as the submarine started sinking".
FILE - This is a April 30 2008 file photo of submarine owner Peter Madsen.
Early Friday, Danish authorities announced they were looking for the Nautilus, which had been reported the previous evening in the Oresund strait between Denmark and Sweden, with two people.
He denies any involvement in the disappearance of 30-year-old Kim Wall who had been on board the 60ft-long vessel before it sank. She also was not identified by name. Divers were initially unable to safely enter it.
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.
"My passion is finding ways to travel to worlds beyond the well-known", Madsen wrote on the site.
"The undersea world is close, it's handsome, always just around the corner in Denmark".
The Nautilus set out from Refshale Island, a former shipyard redeveloped as an entertainment and activity spot, at about 7 p.m. local time on Thursday, according to a police timeline.
"A radio contact was established for the boat, which, according to the owner, was heading towards the harbor", the police statement said.
"So far it hasn't been possible to see what there is inside the submarine", it said. The Navy said it was spotted sailing but then sank.