Nguyen Van Nhan, Bui Dinh Viet and Bui Tien Tung drove to a mountainous area in An Phu Commune in My Dinh District with a gun to hunt birds last Monday.
They saw two goats roaming free on a hill, shot them dead and put them in their car.
When they were about to leave the area and reached Ai Nang Bridge, they were stopped by locals and asked for an explanation.
The officers claimed to have shot the goats "by mistake," and it is now being investigated.
Senior police officials and other authorities Tuesday called on the family that owned the goats to placate them and apologize for the incident.