Peter Madsen (below) denies killing the Swedish woman, saying he last saw her when he dropped her off on the tip of an island in Copenhagen late on Thursday.
Madsen told police he had dropped off Wall not far from where their journey began, but after she was later reported missing, authorities suspected she may have been inside the submarine when it sank.
"The owner of the submarine was arrested and is accused of having killed the Swedish woman without intent", the police statement said.
Miss Wall is a freelance journalist who graduated with a masters from Columbia University before going on to write about identity, gender, pop-culture, social justice and foreign policy.
The 40-ton, 18-meter long Nautilus, one of three subs built by Madsen, is now sitting under 7m (24ft) of water with divers unable to enter it safely.
Madsen (46) financed his submarine project through crowdfunding and completed the submarine, the UC3 Nautilus, in 2008.
Two helicopters and three ships scoured the Baltic Sea waters between Copenhagen and the island of Bornholm.
Police said the submarine was on the seabed in Koge Bay, south of Copenhagen, at a depth of seven meters.
Footage aired on Denmark's TV2 channel showed Madsen, 46, getting off what seemed to be a private boat and making a thumbs up sign as he walked away.
"Whether the woman was on board the submarine at the time of her disappearance is unclear", police said.
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.
He is now being held on preliminary manslaughter charges with a judge set to rule on Saturday whether he must remain in detention while investigations are carried out.
He said there had been a problem with a ballast tank that "turned into a major issue".
"I am fine, but sad because Nautilus went down".
"It took about 30 seconds for Nautilus to sink, and I couldn't close any hatches or anything", Madsen said.
Deputy Insp Jens Moller Jensen said investigators were looking for witnesses who may have seen the woman after the time Madsen said she disembarked.