"We're not just looking at pricing problems, but also possibly availability problems of food," Beasley told a UN Security Council meeting.
While speaking of the humanitarian situation in Ukraine, Beasley urged against ignoring humanitarian crises in other parts of the world.
"We are starting to cut rations for millions of children and their families across the world," he said, adding that the crisis in Ukraine is "the catastrophe on top of the catastrophe."
Beasley estimated that humanitarian workers will reach 2.5 million people in dire need of food in Ukraine over the next couple of weeks and by the end of June this number will total 6 million.
"We can't neglect Africa, Middle East though, or else there'll be migration on all sides of Europe," he said.
On Monday, the International Organization for Migration said that almost four million people, including 200,000 third-country nationals, have left Ukraine during Russia’s military operation in the country.