The baby who has been named Miracle weighed 2.8 kg (6.1 lbs), and was born on the Aquarius, a rescue ship chartered by the group.
"Happy news from the #Aquarius this afternoon with the birth of a healthy baby boy!" the NGO tweeted. "Baby Miracle was born at 3.45pm, weighing 2.8 kgs, bringing the total number of rescued people to 70," it added.
Both the baby and his mother, whose nationality is not known, were doing well and were due to reach the port of Catania in Sicily on Sunday.
The child is the 36th baby to be born on board one of the ships that patrol the Mediterranean rescuing migrants attempting to reach Europe in search of a better life.
The Italian coastguard said nearly 1,500 migrants had been rescued on Thursday and Friday alone.
The rescues were in addition to the 10,800 new arrivals already registered in Italy since the start of the year, according to International Organisation for Migration (IOM) figures.