The migrants were among a group of over 40 Somalis, including a 10-year-old boy and 21 women, travelling towards the southern Italian region from Greece, Corriere reported.
Survivors claim the traffickers hurled the seven people overboard before abandoning the boat in the early hours of Monday.
The body of a woman was later found near rocks near Capo di Leuca, one of three areas where the migrants were said to have been thrown into the sea.
Italy has taken in some 320,000 boat migrants since the start of 2014.
In 2015, however, the main focus of the migrant crisis shifted to Greece with refugees from the Middle East arriving there via Turkey in much larger numbers.
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Over a million migrants reached Europe in 2015, most of them refugees fleeing war and violence in Afghanistan, Iraq and Syria, according to the United Nations refugee agency.
At least 3,692 have died attempting to make the crossing, according to a count by the International Organisation for Migration (IOM).