Anne-Elisabeth Falkevik Hagen, 68, has been missing since October 31, chief investigator Tommy Broeske revealed on Wednesday, with police saying she was abducted "against her will".
"A ransom demand and serious threats have been issued", Insp Tommy Brøske told reporters.
Since the end of October past year, Anne-Elisabeth Falkevik Hagen, wife of Norwegian billionaire Tom Hagen, has been missing.
Investigators refused to confirm that amount but said they advised the family not to pay the purported kidnappers.
The Norwegian police have reportedly been forced to use civilian cars with fake license numbers when moving in the area around the couple's residence outside of Oslo, in order not to arouse suspicion in case the suspected kidnappers might have been watching.
Quoting unnamed sources, Norwegian newspaper Verdens Gang reported that the unidentified plotters-whether they are holding Hagen or not-have demanded a ransom of just over $10 million in the Monero cryptocurrency. Since then, police had received "more than 100 tips", Broeske said, adding "several seems to be interesting" without elaborating.
Anne-Elisabeth Hagen, 68, the wife of real estate investor Tom Hagen, went missing on 31 October, but news of her disappearance had not previously been disclosed.
Lindsay Lohan too busy with her night club for drugs and alcohol
The Mean Girls star said she isn't sure she would be able to recreate the dance. People have a different approach. and I really admire it.
The missing woman's husband, Tom Hagen, also 68, is Norway's 172nd richest man, according to the magazine Kapital, with an estimated fortune of 1.7 billion kroner (174 million euros, $200 million).
"The family made a decision to follow the police advice", Svein Holden told reporters. He made his multi-millions in the real estate and energy industries.
Police were due to give a press conference on the matter later Wednesday.
Tommy Broeske, a Police Inspector said that, at present, their goal is to find the missing woman "alive and reunite her with the family".
The couple lived a quiet life away from the public eye, according to local media reports. Mr Broeske said they were working with Europol and Interpol on the case.
Such events are extremely rare in the Scandinavian country, which enjoys a generally low crime rate.