Helicopters were also deployed to rescue seven people in the more remote towns of the Apennine Mountains, which form the backbone of central Italy.
Floodwater invaded garages and bases and with its weight and force knocked down doors.
“It was an extreme event, more than an exceptional one,” climatologist Massimiliano Fazzini said.
He said that based on his calculations the amount of rain that fell, concentrated over four hours that included an especially heavy 15-minute period, was the most in hundreds of years.
In a space of a few hours, the region was deluged with the amount of rainfall it usually receives in six months, state TV said.
Some of the worst flooding struck in and around town of Senigallia, where a river overflowed its banks.
Hamlets in the hills near the Renaissance tourist town of Urbino were also inundated when fast-moving rivers of water, mud and debris rushed through streets.