Zebras cannot throw up as they don't have the nerve muscles for throwing up like humans and other animals have.
It's not possible for Zebras to throw up because they do not have the mechanism inside them like humans and some other animals do.
If a Zebra eats anything that is poisonous to them then it can easily be fatal to them as they won't be able to vomit up the thing that they ate that was poisonous.
Zebras belong to the same family as equine and horses which cannot throw up either.
Neither the Zebras or the horses have the nerve muscles or muscles to allow them to throw up so without those nerve muscles and muscles the ability to throw up is not possible.
Zebras are African equines with distinctive black-and-white striped coats.
There are three living species: the Grévy's zebra, plains zebra, and the mountain zebra.
Zebras share the genus Equus with horses and asses, the three groups being the only living members of the family Equidae.
Familiarity with human hunter gatherers may also have fostered a strong avoidance response in the zebra.
All of this means that zebra are not really “people friendly” and as a species they do not fit the criteria for domestication.