The foal's body was found at the edge of a waterhole.
It is illegal in the United States to shoot wild horses.
The body was found on Wednesday by Craig Downer, a wildlife ecologist and Cloud Foundation Board member, and Chrystie Davis, a wild horse advocate.
Davis, an experienced horsewoman, examined the foal for any broken bones. What she found was an apparent rope burn on a rear leg as well as a gunshot wound.
"It seems as though the foal was shot in the gut," Davis said. "It looked as though the foal was abused, lassoed around the hind legs and dragged."
Photographs were taken of the body.
The Cloud Foundation said it was seeking information from the bureau about a white stallion which it understood had suffered head trauma, supposedly from fighting during transport.