He has denied responsibility for the fate of 30-year-old Kim Wall, saying she had disembarked before his vessel went down.
Nautilus, named after the ship from the classic science fiction novel Twenty Thousand Leagues Under the Sea, was built by Mr Madsen after raising $200,000 (£154,000) online.
According to a statement Wall's family shared with CPJ today, the 30-year-old Swedish-born journalist, who was based in NY and Beijing, was working on a story about inventor Peter Madsen when she went missing.
The family of a journalist who has been missing since she joined the inventor of an amateur-built submarine on a voyage in Denmark says she freelanced for prestigious publications such as the New York Times, The Guardian and Vice Magazine.
In a statement to Swedish paper Aftonbladet, Ms Wall's family said: "It is with great dismay we received the message that Kim is missing".
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.
Copenhagen Police confirmed the charges on Friday evening, but its divers have been unable to enter the submarine thus far.
"He then climbed down inside the submarine and there was then some kind of air flow coming up and the submarine started to sink", Isbak said.
Madsen had wanted to launch himself into the space race before building his submarine the Nautilus, the biggest privately-made one ever when he made it in 2008.
Its owner Madsen was rescued shortly before, but there was no sign of the Swedish journalist.
Madsen says he dropped her off before the sinking.
They described her as "160cm tall, 56kg, 30 years old, with reddish-brown hair and green eyes".
It was the journalist's boyfriend who alerted authorities early Friday that the sub had not returned from a test run, police said. Half an hour later "the submarine suddenly sank and the owner was subsequently rescued on a private motorboat sailing him in port".
Madsen told authorities he had dropped the woman off on an island in Copenhagen's harbor a few hours into their Thursday night trip.
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