The crew on the Aquarius ship had rescued 946 people and was travelling to Italy when the mother, Taiwo, went into labour.
Mercy - as the little girl was named - is the fourth baby to be born aboard the Aquarius.
The birth went smoothly and Mercy, weighing a healthy 3.7kg (8 ounces), disembarked in Catania with her mother later on Tuesday. Italian authorities and relief organizations were on hand to assist the rescued migrants.
"Giving birth to a child is one of the most intimate moments in a woman's life, and she had to go through it on a boat surrounded by complete strangers”, said midwife Elizabeth Ramlow, who was aboard the boat.
Monday and Tuesday's rescues came after a busy weekend, which saw over 3,000 people rescued in one day as migrants take advantage of milder weather to attempt the risky crossing.
The total of 947 brought to shore on Tuesday - including Mercy and 200 unaccompanied children - was a record for the Aquarius boat, coming as aid organizations have raised fears that spring could see a further increase in the number of migrant arrivals.
Worsening conditions in Libya are thought to be driving the surge in arrivals, together with fears that the oversea route could soon be closed.
In February, Italy and Libya signed an EU-backed memorandum of understanding under which Italy's coast guard will help train and equip its Libyan equivalent to make it more effective in stopping boats.
But this may have had the immediate effect of encouraging more migrants to make the risky journey, as they fear the Libyan coastguard would simply bring them back to Libya.
Photo: Andreas Solaro/AFP