"Search underway since last night for a 5-month-old baby and grandmother missing due to flooding of Sterza creek in Montecatini Val di Cecina", near Pisa, firefighters said on X.

"Father, mother, grandfather rescued on a rooftop", they said, adding that they were "foreign tourists".

Montecatini Val di Cecina's mayor Francesco Auriemma told AFP the family was from Germany.

The holidaymakers were caught off guard by the sudden breaking of the river's banks during heavy rains which swept through the area late Monday, rescue workers said.

Firefighter divers were searching the area with the help of a helicopter, drones and sniffer dogs.

"The flood was very violent and the creek swelled abruptly... completely swamping the house occupied by the German family," fireman Nicola Cinnelli told ANSA news agency.

"The child slipped out of the arms of the grandma", who was then swept away as she tried to recover the baby, mayor Auriemma told the Corriere della Sera daily.

Heavy rains have severely flooded several areas in northern Italy this month.

Experts say man-made climate change is making extreme weather such as storms more frequent and intense.