Dramatic footage posted on social media shows rivers of mud flowing through the town of Bitti in Nuoro province.
Italian media say the three who have died there include an older man who drowned at home and a man killed in his vehicle.
Strong winds and rain have battered the island since Friday, cutting off power and forcing some people to evacuate.
Andrea Soddu, mayor of the province's main town of Nuoro, warned of "particularly heavy" rainfall in the area and asked citizens to exercise "maximum caution" in a post on Facebook.
One reporter from local newspaper La Nuova Sardegna posted footage of the flooding in Bitti.
There are also fears of flooding in the nearby towns of Torpè and Galtellì with further rains expected on Saturday.
Emergency services have moved some 150 residents of Galtellì to municipal facilities, Mayor Giovanni Santo Porcu told ANSA news agency.
"We are monitoring the situation but first of all we are trying to protect public safety," he reportedly said.
In 2013, heavy flooding caused by Cyclone Cleopatra killed at least 18 people in Sardinia.