Al-Baker will start his one-year term in June next year. He will be taking over from Singapore Airlines Goh Choon Phong.
IATA is a trade association representing 275 airlines that carry an estimated 83 per cent of the worlds total air traffic.
The closure of airspace in Bahrain, the UAE and Saudi Arabia has forced Qatar Airways to fly longer routes since June, in addition to stopping all flights to the blockading countries.
Earlier this month, the UNs International Civil Aviation Organisation (ICA) indicated Bahrain and the UAE have agreed to open some of their airspace to Qatar Airways.
The airspace under consideration was later confirmed as the airspace above the international waters that the UAE and Bahrain manage. The blockading countries sovereign airspace remains closed to Qatar-owned and Qatar-registered aircraft.
On 8 August, Qatar Airways began its three weekly flights between Doha and Sohar International airport in Oman.
Qatar Airways envisages the new Doha-Sohar to help offset the Doha-Dubai route, which has been discontinued as a result of the embargo imposed on Qatar.
Sohar is located about 173 kilometres from Dubais airports. Flying time between the airports is estimated at up to 30 minutes.