The barges were carrying about 3,800 pounds (1,725 kilograms) of phosphate fertilizer between them, local media report.
A significant amount of the fertilizer got into the water, but it is expected to dilute quickly because of the river's heavy flow, according to Jay Wright, environmental programs manager for the Oklahoma Department of Environmental Management, as quoted by AP news.
The allision did not break the dam, but the Army Corps of Engineers will inspect further for any damage.
Powerful storms have hit the central US, including a system that spawned deadly tornadoes overnight.
The wet weather has caused heavy flooding, and the threat from swollen waterways persists.
One unoccupied home rolled into the river. One death has been attributed to the flooding in Oklahoma.