Kim Wall, 30, vanished after having boarded the 18-metre Nautilus sub on Thursday evening, apparently as part of her work on a feature story about its owner, inventor and entrepreneur Peter Madsen.
"The investigations confirm that the sinking of the submarine was ostensibly a consequence of a deliberate act," Copenhagen police said in a statement.
Early Friday, Danish authorities announced they were looking for the Nautilus in waters off Copenhagen.
The vessel was located in a bay in Køge, some 50 kilometres south of the Danish capital. Just after being found, Madsen was rescued and the submarine suddenly sank.
Madsen said in media interviews after his rescue that the sub encountered a problem with the ballast tank.
The Nautilus was refloated and towed to the Copenhagen port on Saturday, then emptied of water overnight. On Sunday police entered the sub and found it empty.
Madsen, who describes himself on his website as an "inventrepeneur", claims he dropped off Wall on Refshaleøen island on Thursday after she had completed her interview.
The 46-year-old is accused of negligent manslaughter and was on Saturday remanded in custody for 24 days. He denies the charges and his lawyer says her client is "hurt" by the accusation.
Wall is a freelance journalist based in China and the US. Her articles have appeared in the New York Times, the Guardian and Vice, among others.
"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 homicide police chief Jens Møller Jensen said Sunday.
Friends of the missing journalist told broadcaster TV2 on Monday that they feared the outcome of her disappearance.
“The worst thing would be if she was never found, and we never get answers,” Wall's friend Malin Franzén told TV2 Lorry.
“She wrote many unusual stories and visited subcultures, so when we heard about this story, before we knew Kim was involved, we actually thought it was right up her street,” Franzén said.
Sebastian Dahl Lundbergh, Franzén's boyfriend and also a friend of Wall's, said that it was “impossible” that she was keeping herself hidden from authorities.
“I have read on the internet people speculating that she's hiding on purpose. That's unthinkable,” he said.
“Something has happened to her, and I truly hope that the police find her, either dead or alive. She had great plans for the future,” Franzén added.
Swedish and Danish authorities are cooperating on the search for the missing reporter.
Madsen, who was described in a 2014 book as "Denmark's Do-It-Yourself Astronaut", had wanted to launch himself into the space race before building the crowd-funded Nautilus, the biggest privately-made one ever when he built it in 2008.
Police have now asked for anyone who has previously sailed in the submarine to come forward with information.
Police are keen to learn more about how previous trips with Madsen in the submarine were conducted out and which routes were taken, according to the press statement.
Submarine disappearance timeline: What we know so far
Thursday 7pm: The submarine, crewed by its owner Peter Madsen and a Swedish journalist, sails from the Refshaleøen island harbour near Copenhagen.
Thursday 8:30pm: Denmark military authorities receive a message from a cruise ship that observed the submarine sail out of Copenhagen Harbour, according to a DR report.
Thursday night: Nautilus is spotted sailing unusually close to a freight ship with its external lights switched off, according to an anonymous report provided by a witness to Swedish daily Aftonbladet.
Friday 2:30am: The partner of the Swedish woman reports that the craft is missing. The Danish Defence Command (Værnsfælles Forsvarskommando) begins searching for the submarine.
Friday 10:30am: The submarine is sighted in Køge Bay. Radio contact is made and the owner says he is setting course to Copenhagen, and that the submarine has technical problems.
Friday 11:00am: The owner is recovered by a private boat, but there is no sign of the second crew member. The owner is sailed to land at Dragør Harbour.
Friday afternoon: Police in Sweden state that a missing person alert issued during the morning pertains to the woman on board the submarine and remains in place, reports Swedish news agency TT.
Friday 5:44pm: Copenhagen police announce through a press statement that the owner of the Nautilus has been charged over the woman's death. Police divers have located the sunken submarine but have not yet gained access to it.
Saturday afternoon: Madsen is remanded in custody for 24 days by Copenhagen City Court as work to raise the submarine begins and the identity of the woman emerges as journalist Kim Wall, after her family contacts Danish media.
Sunday: The raised submarine is brought to land and police technicians begin their examination, but no body is on board.
Monday 9:30am: Madsen's lawyer informs media that her client accepts his preliminary detainment on charges of manslaughter.
Monday 2:26pm: Following technical examination of the wreck, police announce that they believe the submarine to have been deliberately sunk.