Five other migrants suffered injuries and were taken to hospitals, health authorities in the Italian port city of Crotone said, adding that two of them were in serious condition.
Two finance guard agents were injured as they tried to rescue the migrant boat, a commander told the AdnKronos news agency. He said the ship's engine went on fire and then there was an explosion.
According to him, the search was continuing to make sure that everyone had escaped.
Italy was once a major route to Europe for hundreds of thousands of asylum seekers and other migrants, but their numbers plummeted following an operation in Libya against smugglers.
However, during 2020 there has been an increase in the number even though Italy has closed ports to migrant ships, saying it is impossible to help them due to the coronavirus crisis.
About 18,000 migrants have arrived on the shores of Italy this year, according to official data from the interior ministry, compared to about 4,900 in the same period of 2019.