In a statement, the authority also said licences granted to Qatar Airways' employees would be withdrawn.
Saudi Arabia had already suspended flights to and from Qatar on Monday, amid a diplomatic row between the kingdom and Qatar.
Qatar Airways is wholly owned by the Qatari government. The airline group employs more than 40,000 people worldwide.
The chief executive of Qatar Airways, Akbar al-Baker, is also a non-executive director of Heathrow Airport Holdings, which operates London's biggest airport.
Flight hubSaudi Arabia and several other countries have cut ties with Qatar, accusing it of supporting terrorism in the Gulf region.
Other neighbours, including the United Arab Emirates (UAE), have closed their airspace to Qatari planes.
Six countries - Bahrain, Saudi Arabia, the UAE, Yemen, Libya's eastern-based government and the Maldives - cut diplomatic ties with Qatar on Monday.
Bahrain, Saudi Arabia and the UAE have given Qatari nationals two weeks to leave and banned their own citizens from travelling to Qatar.
Doha, Qatar's capital, is a major hub for international flight connections.
Other airlines affected by the airspace restrictions include Qatar Airways, Etihad Airways and Emirates.
When avoiding Saudi Arabia, their massive - and only - neighbour, Qatar's planes are having to take more indirect routes, leading to longer flight times.
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