The woman was a journalist writing about Madsen and his submarine, Swedish and Danish media reported.
The decision to rescind Madsen in custody for a further 24 days was made by a judge after a two-hour custody hearing.
Madsen's defence lawyer, Bettina Hald Engmark, said her client maintains his innocence.
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.
Kim Wall's family said in statement emailed to The Associated Press on Saturday, "It is with great dismay that we received the news that Kim went missing during an assignment in Denmark". Her family had not heard from her.
The Sweden-born freelance journalist 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.
The submarine's Danish inventor, Peter Madsen, is being held on suspicion of manslaughter in Wall's disappearance.
According to a statement Wall's family shared with CPJ today, the 30-year-old Swedish-born journalist, who was based in NY and Beijing, was working on a story about inventor Peter Madsen when she went missing.
At Least 15 People Killed in Northwestern Pakistan Blast
The ISPR confirmed that seven civilians were among the 15 martyrs, while 25, including 15 civilians, were injured in the attack. The blast occurred at a bus stop in the provincial capital Quetta and the area caught fire soon after the explosion.
Authorities were alerted that something had gone wrong with the submarine by Miss Wall's boyfriend after she failed to return home, prompting a major search operation involving two helicopters, three ships and several private boats.
Madsen, whose submarine sunk near Køge on Friday, denies the charges.
While the UC3 Nautilus was going down, Isbak says "came up again, stayed in the tower until water came into it as the submarine started sinking".
Its owner Madsen was rescued shortly before, but there was no sign of the Swedish journalist.
Danish police said on Saturday they were preparing to search a sunken submarine owned by Danish inventor Peter Madsen who has been charged with the inadvertent manslaughter of a journalist. 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. He has denied responsibility for the 30-year-old woman's fate, saying she disembarked earlier.
"It took about 30 seconds for Nautilus to sink, and I couldn't close any hatches or anything", he said.
Madsen told authorities he had dropped the woman off on an island in Copenhagen's harbor a few hours into their Thursday night trip.