The woman was a journalist writing about Madsen and his submarine, Swedish and Danish media reported.
Peter Madsen is being investigated over the disappearance of journalist Kim Wall who was on the £154,000 UC3 Nautilus submarine shortly before it was wrecked.
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.
Wall's boyfriend alerted authorities early on Friday the submarine had not returned to Copenhagen as expected, sparking a major search involving two helicopters, three ships and several private boats.
Copenhagen Police confirmed the charges on Friday evening, but its divers have been unable to enter the submarine thus far.
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".
Mr Madsen initially said that he dropped Ms Wall off before it sank but police say he has now changed his statement - although they have not said what to.
Before his arrest, Madsen appeared on Danish television to discuss the submarine's sinking and his rescue.
"Whether the woman was on board the submarine at the time of her disappearance is unclear", Danish police said without naming her. "But I guess that was pretty good, because I otherwise still would have been down there".
"We're still hoping that we'll find Kim Wall alive, but we are preparing ourselves for the fact that she may not be", Copenhagen police homicide chief Jens Moller said. "They were the only two on board yesterday".
According to the Copenhagen Post, a search of the vessel is likely to be carried out once it has been towed to port later on Saturday.
Madsen describes himself as an "inventrepaneur" on the website for his Copenhagen-based company. "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". It was spotted by a lighthouse in Koge Bay, a seaport south of the city, at 10:30 a.m.
Before the submarine's relaunch, Madsen had been locked in a fierce ownership dispute with a board representing the group of volunteers who helped him build it.
He has said the submarine developed a problem with the ballast tank.
Lisa Leff contributed from London.