Italy’s fire and rescue agency, Vigili del Fuoco, said a boat ran aground near the village of Staccato di Cutro.
It reported there were about 40 survivors and said support for the migrants was ongoing.
Several Italian news agencies, including ANSA, reported that about 30 bodies have been found on the banks of the village in the province of Cotrone, Calabria.
The AGI news agency said a baby was among the dead.
The Italian news agency Adnkronos reported that the boat, carrying migrants from Iran, Pakistan and Afghanistan, hit rocks during rough seas.
Coastal rescue services were unavailable to provide additional details.