It was later spotted but sank on Friday morning and Mr Madsen was rescued.
The journalist had been writing about Mr Madsen and his submarine, which at one stage was the largest privately-made vessel of its kind.
Madsen's defence lawyer said her client maintains he is innocent but is "willing to cooperate" and has not decided whether to appeal the ruling. "I would very much like to express myself", he said after the preliminary charges were read.
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.
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.
Mr Madsen is due to appear before a judge on Saturday.More news: Paul Scholes questions Chelsea's decision of selling Matic to Man United
However, Swedish police said later on Friday they were investigating the whereabouts of a missing woman who had been on the submarine at some point. The inventor has denied wrongdoing and said that he dropped Wall-who was reported to be the only other person on board the submarine with him-off on an island close to Copenhagen Thursday night before the submarine sank, according to AP reports. "[He] came up again and stayed in the tower until water came into it".
"It is with great dismay that we received the news that Kim went missing during an assignment in Denmark", her family said in statement emailed to The Associated Press.
The 30-year-old Sweden-born freelance journalist had 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.
A look at her Facebook page reveals she has written stories all over the world for the likes of the New York Times and the Guardian.
A salvage vessel, the Vina, was Saturday working on raising the submarine, which was seven metres under water off Copenhagen's south island of Dragoer. It can carry up to eight people and can dive up to 470m, although in practice it has rarely gone beyond 40m.
If tried and found guilty, Madsen would face between five years and life in prison.