The Saudi Press Agency said the Saudi government would also reach out to its allies "and start the immediate legal procedures for understanding with fraternal and friendly countries and global companies to implement the same procedure as soon as possible for all means of transport to and from the State of Qatar, for reasons related to Saudi national security".
Oil giant Saudi Arabia accused Qatar of backing militant groups - some backed by regional arch-rival Iran - and broadcasting their ideology, an apparent reference to Qatar's influential state-owned satellite channel Al Jazeera.
Gas-rich Doha, which has long exercised an independent streak in its foreign policy, last month denied comments which appeared on its official news agency questioning United States hostility towards Iran.
India will not be impacted by some Gulf countries cutting off diplomatic ties with Qatar, external affairs minister Sushma Swaraj said on Monday.
"(Qatar) embraces multiple terrorist and sectarian groups aimed at disturbing stability in the region, including the Muslim Brotherhood, ISIS (Islamic State) and al-Qaeda, and promotes the message and schemes of these groups through their media constantly", state news agency SPA said.
Qatar Airways was not immediately available for comment.
Economic consequences were already emerging, with UAE carriers Emirates, Etihad, flydubai and Air Arabia, as well as Saudi Airlines, announcing the suspension of all flights to and from Qatar as of Tuesday morning.
There is no doubt, however, about the seriousness of this move for Qatar, a small, desert state that sits on a peninsula in the Arabian Gulf, with a land border with Saudi Arabia to the south.
Qatar reacted with fury, denying any support for extremists and accusing its Gulf neighbours of seeking to put the country under "guardianship".
"One of its pitches (to secure the World Cup) was that Qatar is one of the most stable countries in the Middle East", he told AFP.
Trump recently visited the Saudi capital and addressed 55 Muslim leaders in a landmark speech urging them to double down on efforts to combat terrorism.
The fund, called The Qatar Investment Authority, was founded in 2005 to grow the money made off the OPEC nation's natural resources.
Secretary of State Rex Tillerson and Defense Secretary Jim Mattis, traveling in Australia on Monday, asserted that the developments would not affect the USA -led coalition fighting Sunni extremist groups in the Middle East.