The coastguard saw the boat overnight some 18 miles (29 kilometers) off the coast of Lampione, an uninhabited island near Lampedusa, and rescue operations were conducted, the prosecutor said. His office has opened an inquiry into alleged abetting of illegal migration and manslaughter, he added.
Lampedusa Mayor Salvatore Martello confirmed the death toll, adding the vessel was carrying 280 migrants, mainly from Bangladesh and Egypt.
Italy, a major route into Europe for hundreds of thousands of asylum seekers and other migrants, has seen an increase in migrant boats in recent months.
As of Jan 24, 1,751 migrants have disembarked in Italy's ports so far this year, according to government data.