"He then climbed down inside the submarine and there was then some kind of air flow coming up and the submarine started to sink".
Danish police would not comment on why charges had been brought before a body had been found, but said they would offer another update later on Saturday after Mr Madsen appears in court.
"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.
Hald Engmark says Madsen is "willing to cooperate" and hasn't decided whether to appeal the detention ruling.
Madsen's submarine, the UC3 Nautilus, is reportedly the largest privately-built submarine in the world.
The submarine was first reported missing by Ms Wall's boyfriend, after she failed to return from what should have been a short trip.
"It took about 30 seconds for Nautilus to sink, and I couldn't close any hatches or anything", Madsen said.
Police have identified the missing journalist as Kim Wall, a 30-year-old Swedish woman who was writing a feature about Mr Madsen. "But I guess that was pretty good, because I otherwise still would have been down there".
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. 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.
Kristian Isbak, who had responded to the Navy's call to help locate the ship, sailed out immediately Friday and saw Madsen standing wearing his trademark military fatigues in the submarine's tower while it was still afloat.
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.
"The undersea world is close, it's lovely, always just around the corner in Denmark". The Danish Navy launched a major search involving two helicopters, three ships and several private boats.
"A radio contact was established for the boat, which, according to the owner, was heading towards the harbor", the police statement said.
The vessel sank early Friday morning off the Danish coast as the inventor, Peter Madsen, escaped to a nearby rescue ship.
He has said the submarine developed a problem with the ballast tank.