The wettest year on record is raising costs for the nation’s biggest agricultural companies, stalling farmers’ fieldwork and slowing shipments across the U.S. Farm Belt.

“It’s got to be the worst ever that we’ve seen,” said Jim Collins, head of Corteva Agriscience, the agricultural division of seed and pesticide maker DowDuPont Inc. Corteva’s sales fell 11% for the most recent quarter it reported this month, partly because of Midwestern floods.

The...