UN officials are in talks with the coalition to get permission for the flights to deliver aid to Yemen, where some seven million people are on the brink of famine.
"There were no flight clearances granted to our flights today," said UN spokesman Farhan Haq. "We expected to have two flights going and those are on hold for now."
The coalition sealed off Yemen's borders following a weekend missile attack by Yemen's Houthi rebels that was intercepted near Riyadh airport.
A Houthi transportation minister is reported to have described the closure as a "crime against human rights".
The Saudi-led Arab military coalition intervened in Yemen in 2015 to support President Abedrabbo Mansour Hadi after the Huthis forced him into exile.
The coalition as well as the rebels have been regularly criticized by the United Nations for blocking aid to civilians.
The United Nations has listed Yemen as the world's number one humanitarian crisis, with 17 million Yemenis in need of food, seven million of whom are at risk of famine and cholera causing more than 2,000 deaths.
Last month, the United Nations put the coalition on its blacklist for killing and maiming 683 children during the conflict in 2016 and for carrying out 38 verified attacks on schools and hospitals.