Italy’s institutional agency for the fire and rescue service, Vigili del Fuoco, said a boat ran aground off the village of Staccato di Cutro.
It reported there were around 40 survivors and said support for the migrants was ongoing.
Various Italian news agencies, including ANSA, reported that over 30 bodies were found on the shores of the village in the Cotrone province, Calabria. La Repubblica reported the number to be 34.
The news agency AGI said a baby was among the dead.
Italian news agency Adnkronos reported the boat, carrying migrants from Iran, Pakistan and Afghanistan, hit rocks during rough sea conditions.
The coast rescue services have not been available to provide additional details.