The Saudi government's move follows coordinated action on Monday by Saudi Arabia, Egypt, the United Arab Emirates and Bahrain to cut ties with Qatar.
Saudi Arabia's General Authority of Civil Aviation (GACA) said in a statement any licences granted to Qatar Airways employees would also be withdrawn.
A few hours later Bahrain announced it had cancelled licences granted to Qatar Airways and had also asked the airline to close its offices within 48 hours, the official Bahrain News Agency reported.
Saudi Arabia's aviation authority said customers seeking adjustments on tickets to or from Qatar should communicate with the company by phone or through its website.
Dozens of people crowded into the Qatar Airways office in central Riyadh on Tuesday morning, asking for refunds or to be re-booked on flights with other airlines.
"We’re trying to get refunds, but the problem is the logistics. Now if you want to re-book, how are you supposed to deal with the hotel booking, the rental car, the visa?" Ganas al-Ganas, a Saudi national planning a trip to Europe, said.
The suspension of flights comes three weeks before the start of the Eid holiday week, a popular time for travel in the Gulf.
Qatar Airways said on its website it had arranged three chartered Oman Air flights to transport passengers from Jeddah to Muscat on Tuesday. A connecting Qatar Airways flight would then take them onwards to Doha.
The airline also cancelled flights to Bahrain, Egypt and the United Arab Emirates on Tuesday, the day after it had suspended flights to Saudi Arabia.
A man walks past Qatar Airways office in Manama, Bahrain.
Saudi Arabia and Bahrain on Tuesday revoked the licences of Qatar Airways and ordered its offices to be closed within 48 hours, as the two Gulf Arab states severed transport links with Doha in a diplomatic row.
