A source close to the police investigation told Brazilian magazine Veja the criminals have stipulated the ransom money be paid in pounds sterling and split into four plastic bags.
The amount is the largest ever demanded in a kidnapping in Brazil, which sees hundreds of cases a year.
Ecclestone, 85, met Fabiana, 38, in 2009 in the run-up to the Brazilian Grande Prix in Interlagos, where she was working as marketing director for Brazil's Formula One.
The couple wed three years later after Ecclestone divorced his wife of 25 years, Croatian model Slavica Radic, to marry the young Brazilian.
Fabiana and her mother, who continued living in the Interlagos district of Sao Paulo, are close.
In a Facebook post on Mother's Day, she wrote: 'Happy Mother's Day to all mothers, and especially mine. There are no words to thank so much love and dedication. Thank you Mum, I love you.'
Fabiana, who is friends with Sky Sports F1 reporter Natalie Pinkham, and Ecclestone live in London. They haven't released a statement on the abduction.
Olympic host Brazil is struggling to show all will be well with the Games to open in Rio on August 5, despite low ticket sales and general public apathy amid a deep recession.
Fears for the safety of athletes have also been raised after two members of the Australian Paralympic sailing squad were robbed at gunpoint.
Last month, Paralympic sailor Liesl Tesch and team official Sarah Ross were confronted by two men while riding their bicycles in at Rio park.
One of the men was carrying a pistol and the women were robbed of their bicycles.
Ecclestone is the UK's fourth richest person with an estimated NZ$3 billion fortune, and one of the most powerful people in sport.
He married for the first time in 1952, aged 21, to telephone operator Ivy Bamford. The pair had one daughter, Debbie, who is now 59, before they split up in the 1960s.
He went on to have a 17-year relationship with Tuana Tan, from Singapore, and was was with her when he began an affair with Croatian model Slavica Malic in 1982.
They wed three years later and a year after the birth of their first daughter Tamara. They went on to have a second daughter, Petra, In 1988.
The couple's undisclosed 2009 divorce settlement - estimated at more than £594million - was probably the largest in UK history.
Bernie and Fabiana began dating in 2009 following the end of his 23-year marriage to Slavica.
The couple announced their engagement in April 2012, with Fabiana seen wearing a £100,000 ring, before exchanging vows that August.
Born in Suffolk to a trawlerman, Ecclestone started his career after the war trading motorcycle parts
Ecclestone, who owns a £23 million chalet in the Alpine skiing hotspot Gstaad, prides himself on his thrift and once said: 'I rarely buy anything without a discount.'
He also rarely buys anything that he does not keep in mint condition. He once said: "Order is a big thing with me. If a picture is crooked, I have to straighten it. It applies to all sorts of things... ornaments, artwork.
"If I were in someone else's house, I'd be the same. I have to go over and fix it. I suppose it's about control. I feel I have to be in control. It's the same with work."
In October 2013 Ecclestone sold his Gulfstream G650 business jet, capable of flying non-stop from the Far East to Britain, for £43m to Leicester City owner Vichai Srivaddhanaprabha
In 2014 Ecclestone paid £60million to a German court to end a trial in which he was accused of bribing a German banker with £26million to ensure a company he favoured could buy a stake in F1.
Mr Ecclestone refused to comment when approached by MailOnline.
