It happened around 7 a.m. Police say a driver passing by the zoo saw the dogs trying to get in and called police.
Ouachita Parish Animal Control officers responded to the area. Two of the animals were destroyed at the scene by animal control officers.
The other two animals were taken into custody and later taken to the Parish Animal Shelter.
In February, five animals at the zoo were killed by a pack of pit bulls.
The dogs killed a Guanaco, an Addax and three other animals on loan from other zoos.