Qatar Airways chief Akbar Al Baker hurriedly left a conference of aviation executives suddenly after news of the crisis in his country broke.
The high profile Al Baker was seen at a lavish welcome function at a hotel resort in Cancun, Mexico on Sunday night (Monday NZT) but wasn't at the meeting the following day.
Saudi Arabia, Bahrain, the United Arab Emirates (UAE) and Egypt announced they were breaking diplomatic relations with Qatar and told their nationals to leave the emirate within two weeks.
Saudi Arabia, Bahrain and Egypt closed all transport links with Qatar, banned Qatari planes from landing and forbade them from crossing their air space.
They allege the government of Qatar supports Islamic extremists in the region, claims that Qatar denies.
It was reported Al Baker flew out on a private plane from the International Air Transport Association conference.
Asked about the Qatar crisis, IATA director general and CEO Alexandre de Juniac said: "We are not in favour of bans and we would like to see connectivity restored as soon as possible."
Qatar Airways began flying to New Zealand in February and its flights would have to avoid Saudi airspace according the terms of the ban.
Flight Centre said it had received calls from worried travellers.
Its general manager of product, Sean Berenson, said there would be very few travellers from New Zealand affected by the announcement.
''For anyone due to be flying on Qatar Airways (ie. up to Europe) it is business as usual.''
A Qatar spokeswoman said early today the airline had suspended all flights to Saudi Arabia, UAE, Kingdom of Bahrain and Egypt until further notice.
''Qatar Airways operations are running as normal with no disruptions to flights with the exception of those to the four countries Qatar Airways has been restricted to fly to.''
In response to these restrictions Qatar Airways had arranged for three charter flights departing Jeddah to Muscat in order to help its passengers in Saudi Arabia.
''We encourage all Qatari passengers stranded to make their way to King Abdulaziz International Airport to avail of these three flights today,'' she said.
The diplomatic crisis is another blow for Qatar Airways which has been hit by the ban on laptops in its planes on flights to the United States.