Does the prefix zoo come from ancient greek word for wandering?

No, the prefix "zoo-" in words like "zoology" and "zoo" does not come from an ancient Greek word for wandering.

The prefix "zoo-" comes from the Greek word "ζῷον" (zoon), which means "animal".

So, "zoology" literally means "the study of animals", and "zoo" is short for "zoological garden".

There is no connection between the prefix "zoo-" and any word for wandering in ancient Greek.