Hippogriffs would be considered as omnivores. The diet of the Hippogriff consists mainly of insects, birds, and small mammals such as ferrets. If Hippogriffs are hungry, they would sometimes paw at the ground for worms if no other food is readily available. You'll know to give your hippogriff something to eat when they do this.

Buckbeak, the famous hippogriff who we all know lived at Hogwarts, eats meat; he has eaten chicken bones, dead ferrets, and dead rats. When in the forest, he dug around in the ground for worms.
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