TOVSTOLUH, Ukraine—Farmers Natalia and Yury Berezovsky have enjoyed two years of record wheat harvests. Now, they have one priority: Stay in business.

Ukraine has weathered war and tough times to deliver its biggest wheat harvests since the fall of the Soviet Union. But the country’s farmers are increasingly squeezed by a weakened currency and bank interest rates near 30%, making it tough to afford essential imports, such as fertilizer, seeds and new machinery.

The pressure is threatening to end a series of bumper harvests that made the country the world’s sixth-largest wheat producer this year—with potentially significant consequences for world markets.

“Our first priority is to stay afloat,” said Mr. Berezovsky, a 45-year-old farmer who used debt to expand his farm from 40 hectares (98.8 acres) in 1994 to 4,000 today. “We don’t have any thoughts to grow.”

Wheat is a crucial staple and politically sensitive export crop in markets around the world, and Ukraine is a major player.