Aparecida Schunk, 67, who is the mother of Ecclestone’s Brazilian wife, Fabiana Flosi, was taken near her home in Sao Paulo, according to reports.
The kidnappers, who are said to be in contact with the Ecclestone family, reportedly want £28million for her safe release.
According to the Brazilian magazine Veja, the captors want the ransom money paid in pounds sterling, and split into four bags.
It is the largest sum of money ever demanded by a kidnapper in Brazil, where there are hundreds of cases each year.
The 85-year-old Ecclestone met his Brazilian wife, 38, in 2009 before the Brazilian Grand Prix in Interlagos, where she was working as a marketing director.
The pair wed three years later, following Ecclestone’s split from his wife of 25 years, the Croatian model Slavica Radic.
Ecclestone and his wife, who live in London, have not commented on the reported kidnapping.