Alan Joyce, the CEO of Qantas Airways who campaigned for marriage equality in Australia, said ensuring a diverse workforce in general could help to drive profits.
Mr Al Baker responded by saying that "it's not in Qatar Airways".
An IATA board photograph published last week featured one woman out of 26 airline chiefs - Christine Ourmières-Widener, chief executive of United Kingdom regional carrier Flybe.Other airline companies have made efforts to promote women to senior positions in recent years.
Brushing off the suggestion that Qatar Airways lack gender diversity, Al Baker declared that a woman is not be capable of leading the airline, owing to the "challenging" nature of the job.
The remarks are not Al Baker's first to spark controversy.
The comment came minutes after Al-Baker - who has a reputation for hitting out at rivals and suppliers over poor performance - had joked that one of his roles as the new chairman of IATA was to be less controversial.
He eventually went on to tell Bloomberg: "We actually encourage women".
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Qatar Airways later issued an official apology on the behalf of Baker claiming that the airlines firmly believes in gender equality. Two-fifths of Qantas Airways' senior management is female, including the heads of the worldwide and frequent-flier loyalty businesses, according to the airline's chief executive, Alan Joyce. Qantas Airways Ltd.'s senior management is 40 per cent female, including the heads of the global and frequent-flier loyalty businesses, CEO Alan Joyce said.
He said recently: "It's the right business thing to do and it's the right moral thing to do".
USA and some European airlines have accused Gulf carriers of unfair competition based on subsidies and social policies, but Walsh - whose group counts Qatar Airways as a shareholder - said he believed Gulf airlines competed on an equal footing.
'Aer Lingus recruited its first female pilot in 1977...
'I think one of the reasons Qantas turned it around so dramatically is that we've embraced diversity'.
When the female journalist then pointed out that a man ran the airline, Mr al-Baker replied: "Of..." It's taken 40 years to get to 10 percent, ' he said at the CAPA-Centre for Aviation summit also taking place in Sydney.
Qatar Airways has been banned from operating in or flying over 18 cities in the United Arab Emirates, Saudi Arabia, Bahrain and Egypt.