Then, in a statement released by the airline, Al Baker portrayed his initial comments as a joke, saying he is known for "some lightheartedness at press conferences".
In fact, during the same IATA press conference, where he made his sexist remarks, the airline's executive promised to abstain from his controversial style, whilst chairing the organization. He was named Qatar Airways' Group chief executive in 1997.
Addressing the International Air Transport Association's male-dominated annual meeting, Al Baker was asked what could be done to address the lack of women in Middle East aviation.
The remarks drew criticism on social media.
The airline pointed to a Bloomberg News interview in which he said he had not meant to refer to all women at the company.
The head of Qatar Airways apologized on Wednesday for saying that a woman could not do his job, while global airlines pledged to speed up efforts to break down gender imbalances in aviation. The carrier has female pilots and female senior vice presidents.
In 2017, he apologised after calling American flight attendants "grandmothers" during a trade row with U.S. airlines, prompting an airline union to accuse him of sexism and age discrimination.
Pressed further as to why being a woman was incompatible with holding the CEO position, Al-Baker said that he was "only referring to one individual" and "not to the staff in general".
He eventually went on to tell Bloomberg: "We actually encourage women".
The CEO of Qatar Airways, where women make up almost half the company's workforce, apologized for saying that a woman couldn't do his job because it was "very challenging".
Cathay CEO Rupert Hogg said there were no immediate vacancies on the top team but there were women managers a level below and diversity was valued at the airline, which has staff from 75 nationalities and is a supporter of the Gay Games 2022 in Hong Kong.
Qatar Airways CEO Akbar Al Baker, who said his job was too hard for a woman, has offered his "heartfelt apologies" for the comments and defended his record of promoting women.
Qatar Airways could face a second straight year of losses in 2018 amid a regional dispute that has banned the airline from four Arab countries, the airline's CEO said on Tuesday.
'We have more diversity on the board now than we have had for a long time, and we have to strive to improve that situation'.
"You know, I have to put a little bit of fireworks around to motivate people to ask more questions", he said.
IATA's board of governors on Sunday.