According to investigators - witnesses say several dogs attacked the goats, though the exact number of dogs is not clear.
The dogs apparently dug a hole under a gate to get to the three goats.
Two of them were euthanized because of their injuries.
Investigators add that city and parish roads are in close proximity to the zoo -- and employees have a direct line to animal control if they should spot any vicious dogs in the area.
Monroe Police say they're getting ready to hire an animal welfare officer - applications will be accepted starting next week.