The police said that Madsen, 46, was being held in custody for 24 days, accused of killing Swedish journalist Kim Wall, 30, who they said had been on his submarine before it sank on Friday.
Madsen was rescued on Friday morning in a navy operation and taken ashore after his homemade 17-meter submarine went down.
The vessel was recovered on Saturday in Koge Bay, south of Copenhagen, at a depth of seven meters, and taken into harbor.
It will be partly drained of water and searched by the police late on Saturday and early Sunday.
Madsen, an entrepreneur known as an artist, submarine builder, and aerospace engineer, went before a judge on Saturday behind closed doors for preliminary questioning. His defense lawyer, Betina Hald Engmark, told Reuters he denied the charges.
The police said on Friday the inventor had said he had dropped Wall off in Copenhagen on Thursday night.
The police in Sweden said they had tried without success to contact her by phone and that her family had not heard from her.
The submarine, the UC3 Nautilus, is one of three constructed by Madsen. It can carry eight people.