Named Miracle, the child was born aboard the Aquarius, a Doctors Without Borders (MSF) ship run in partnership with SOS Mediterranee.
He weighed 2.8kg (6lbs 2oz) and was the sixth baby born on the rescue ship, but the first this year.
Amoin Soulemane, the midwife on the Aquarius, said: “Both the mother and baby are doing very well.”
When baby Miracle was brought up to the deck, the migrants sang and danced to celebrate his arrival.
His mother, whose name has not been revealed, said she was “held captive, beaten, given very little food and extorted for money for release” before she managed to escape her captors in Libya.
She set off to sea on a rubber boat with 68 others on Thursday.
It comes as more migrants attempt to cross into Italy, with more than 1,800 rescued by humanitarian ships in the last three days.
One body was also recovered, an Italian coastguard official said.
Arrivals from Libya have dropped by 85% this year, as Italy provided support to the Libyan coastguard to prevent migrant boats.
But the trend seems to have reversed, and some believe it could be because of good weather.
Lauren King, a spokeswoman from the Aquarius, said: “It’s really hard to know what’s happening inside Libya, or why the Libyan coastguard has not been so active in these last few days.
“Given the weather conditions … It’s better we’re out there and ready.”
The Aquarius brought 70 people ashore in Catania, Sicily on Sunday, and is setting off again for the Libyan coastal waters.
The leader of the far-right League party in Italy, which looks set to form a coalition government with anti-establishment 5-Star Movement, said a surge in arrivals indicated an attempt to undermine the would-be administration.
Matteo Salvani tweeted: “The usual powers that be are threatening us with the migrant boats.”
The League is pledging a hard line on irregular immigration and to deport hundreds of thousands of migrants.