The Brazilian lost his licence after racking up too many penalty points, reports the BBC.
Piquet and his wife Viviane, who also had her licence revoked, must attend a week of lessons to learn good and safe driving conduct, and then pass an exam.
Only then will Piquet - F1 champion in 1981, 1983 and 1987 - be allowed back behind the wheel.
"I think we have to pay for our mistakes, It's not just a speeding problem, I got tickets for all kinds of reasons, like parking where I shouldn't," Piquet told Brazilian media.
The 54-year-old had been seen speeding around the streets of Brasilia in various high-performance cars, including a BMW convertible.
The classes in the Brazilian capital are covering defensive driving, first aid and rules of the road.
Videos highlighting the often tragic consequences of reckless driving are also shown to offenders.
"We're going to make good use of this course and learn something," Piquet said as he and Viviane began their classes on Monday.
Piquet was one of the best-known motor racing drivers to come from Brazil, along with Emerson Fittipaldi and Ayrton Senna.
Piquet's son, known as Nelsinho, is also making a name for himself in motor racing and is the reserve driver for the Renault Formula One team.
