Does Barkskin cast before Wild Shaping apply to your beast form?

Assume you cast Barkskin in humanoid form:

You touch a willing creature. Until the spell ends, the target’s skin has a rough, bark-like appearance, and the target’s AC can’t be less than 16, regardless of what kind of arm or it is wearing.

It is clear that under the rules of Wild Shape “transforming doesn’t break your concentration on a spell you’ve already cast”, but does the effect of the spell carry over to your new skin?