"It is with a great concern that we, her family, received the news that Kim is missing after an interview with Peter Madsen in Denmark", the statement said.
Her boyfriend reported her missing in the early hours of Friday morning saying she had failed to return from her trip.
Madsen had wanted to launch himself into the space race before building his submarine the Nautilus, the biggest privately-made one ever when he made it in 2008.
The 40-ton, almost 18-meter-long (60-foot-long) vessel has been described as the largest privately built submarine of its kind.
Police said the submarine was on the seabed in Koge Bay, south of Copenhagen, at a depth of seven meters.
"Peter Madsen faces preliminary charges (of manslaughter) for having killed in an unknown way and in an unknown place Kim Isabell Frerika Wall of Sweden sometime after Thursday 5 p.m.", Prosecutor Louise Pedersen told a packed courtroom, where proceedings began in a larger hall after delays due in part to overcrowding in another location. The inventor has denied wrongdoing and said that he dropped Wall-who was reported to be the only other person on board the submarine with him-off on an island close to Copenhagen Thursday night before the submarine sank, according to AP reports.
Before his arrest, Madsen appeared on Danish television to discuss the submarine's sinking and his rescue.
"So far it hasn't been possible to see what there is inside the submarine", it said.
Swedish police said later in the day they were investigating the whereabouts of a missing woman who had been on the submarine at some point. "But I guess that was pretty good, because I otherwise still would have been down there". "They were the only two on board yesterday".
By late Saturday the Nautilus had been recovered and was being towed back to Copenhagen.
Madsen describes himself as an "inventrepaneur" on the website for his Copenhagen-based company. "I design and manufacture non-commercial extreme machines, employing teams of volunteering engineers and technicians to challenge the ordinary". "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 expected to arrive in the Danish capital by the end of the evening, said a police statement.
Kristian Isbak tells The Associated Press he had responded to the Navy's call to help locate the submarine on Friday when he spotted Madsen.