I guess juice is considered uncountable here. That feels right to me but I'm not a native English speaker.
The distinction between countable and uncountable might be region-specific though. Where are you from?
In general and without context using "an" would seem a little odd. If the apple juice was in a bottle or carton then you could say "an/a apple juice" because you are referring to the container "a (bottle) of juice".
I also would like to know why it is not also correct to say "an animal drinks apple juice"