More than a hundred emergency rescuers are searching for survivors, the spokesman said, adding that the number of people missing is unknown.
The dramatic gorges carved by the Raganello river are only recommended for experienced hikers, and at certain times of the year, they are rendered off-limits, the AGI news agency reported.
The Civil Protection Department said that 10 bodies were found on Monday, including that of a 14-year-old girl, while another person died in hospital.
Rescue operations started immediately after a small stream near the village of Civita overflowed at 5:30 p.m. local time, he said.
Tourists had packed the Raganello Gorge in the Calabria region when it began to fill rapidly with rain water on Monday.
According to CNN affiliate Rai, a group of hikers exploring a narrow gorge in the Pollino National Park were caught by surprise by the rapidly rising waters.
At least three people are still missing and 23 were rescued of which 11 were taken to the hospital, rescue workers said.
The nationalities of the dead and injured were not yet released, but most tourists and trekkers who visit the area, in the country's deep south, are Italian. "I was lucky, it was an incredible thing".
At its narrowest, it is just a couple of metres wide with walls 400m (1300ft) to 700m (2,300ft) high.
Witnesses say heavy rain in the Pollino National Park area caused a sudden rush of flood water, rocks and mud through the Raganello creek where dozens of hikers had been exploring. The 12-kilometre- (71/2-mile-) long gorge is broken down into three sections, the upper, mid and lower canyons, with hikes averaging between 2 1/2 and 3 1/2 hours.
Guides include spelunkers and rescue instructors, who supply helmets, wetsuits and other equipment.
Mountain rescue squads rushed from the nearest town of Civita to reach the gorge. The disaster followed on the heels of a motorway bridge collapse in northern Italy that killed 43.