You can use the noun zoolatry when you talk about the religious worship of animals. There are many different religions that include zoolatry among their rituals and traditions.
Observant Hindus consider cows to be sacred — this is one form of zoolatry. In Turkic mythology, zoolatry appears in the form of revering wolves, and among some shamans, a belief that certain humans are directly descended from wolves. Zoolatry is a rarely used word that combines the Greek root words zoion, "an animal," and latreia, "worship or service paid to the gods."