The aircraft was cruising at 42,000ft (12,800 metres) when the passenger went into labour.
In a statement, Turkish Airlines said crew had spotted the pregnant woman in pain and quickly responded to assist her, BBC News reports.
Passengers also helped out during the successful birth, which occurred soon after take-off on a service from Conakry in Guinea to Istanbul via Ouagadougou.
Upon landing in the capital of Burkina Faso, the mother and baby, named Kadiju, were taken from the Boeing 737 to hospital.
Both are now reported to be in good health.
Turkish Airlines announced the news of the baby’s arrival on Twitter.
