Anne-Elisabeth Falkevik Hagen, 68, has been missing since October 31, chief investigator Tommy Broeske said on Wednesday, with police saying she was abducted "against her will".
Local police have reportedly scheduled a press conference for later today.
It said Mrs Hagen appeared to have been abducted from the bathroom of her home and that there had been "limited dialogue" with the alleged kidnappers over the internet.
Police declined to comment on the size of the demand.
Multi-millionaire real estate investor Tom Hagen is listed among Norway's richest men, however, his wealth has unfortunately made him and his family a target for cyber criminals.
Norwegian police confirmed that "a woman in her late 60s is believed to have been kidnapped from her home in Lorenskog", around 20 kilometres (12 miles) from Oslo, but did not disclose her identity.
Many Norwegian media outlets knew of Mrs Falkevik Hagen's disappearance but did not publish any details after the police warned against publicising the kidnap over fears the attackers would harm the victim.
"A ransom demand and serious threats have been issued", inspector Tommy Broske told reporters.
"Despite a broad and extensive investigation, we need more information", he continued. The police have also recommended the family not to pay the ransom that was requested in exchange for the promise that she would be released. Police have received no signs whether Falkevik Hagen was still alive, "but we haven't either received any sign that she is not alive", he added.
Norwegian broadcaster NRK says the couple live a "secluded lifestyle" and asked the public to get in contact if any suspicious activity was seen in woodland that surround the family home.
Kidnappings are extremely rare in the Scandinavian nation, which has 5.3 million people and prides itself on low crime rates.
Norwegian authorities are working together with Europol and Interpol on the case.