The kidnappers were reportedly demanding a ransom of $51 million for her release and were in contact with the Ecclestone family, it is claimed.
With under two weeks to go until it hosts the Olympics, the kidnapping is the latest hammer blow to Brazil amid security fears ranging from street crime to militant attacks.
There are increasing fears wealthy visitors will avoid travelling to the country for the event despite a crackdown by police, including the formation of a special anti-kidnap division.
The country is also in the midst of its worst economic crisis in almost a century.
A source close to the police investigation told Brazilian magazine Veja the criminals had 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 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 £3.2billion fortune, and one of the most powerful people in sport.
