De Cesaris, who competed in the 1980s and 1990s for the likes of Alfa Romeo, McLaren and Jordan, lost control of his machine while riding on the city's ringroad, according to a website report by sports daily La Gazzetta dello Sport.
The report said the 55-year-old Italian was travelling on the outside, or slow lane, when he crashed, dying on impact.
De Cesaris's death came on a black day for the sport which saw French driver Jules Bianchi left fighting for his life after crashing at the Japanese Grand Prix in Suzuka.
"All at McLaren send condolences to ex-McLaren #F1 driver Andrea de Cesaris, who sadly passed away today," tweeted McLaren.
De Cesaris started 208 Formula One Grands Prix in his career between 1980 and 1994 but never won a race. He held the unwanted record for having the longest career without a victory.
In a career which saw him drive for 10 teams, he also earned the nickname "Andrea de Crasheris" for his regular involvement in on-track incidents.
The official Formula One website said that in 1982, aged just 22, De Cesaris became the then-youngest driver to start a Grand Prix from the front of the grid after he took his sole career pole, with Alfa Romeo, at the US West race.
His best results were second place finishes at the 1983 German and South African races, again with Alfa Romeo.
After his retirement, De Cesaris became a successful currency trader.