The discovery was made on Sunday afternoon while the apartment, on the edge of the city, was being cleared for sale.
The hand grenade - complete with fuse and detonator - was removed by police and a bomb squad.
While the precise origins of the Second World War weapon were not reported, Ansa said the apartment owner served in the army and died some time ago.
The unusual discovery came less than three months after eight people were arrested over allegedly looting a sunken warship of its bombs.
Members of a mafia clan were accused of robbing explosives from the Laura C Italian Navy ship, which went down off the southern coast during the Second World War.