Are there models of first order Zermelo set theory (axiomatized by: Extensionaity, Foundation, empty set, pairing, set union, power, Separation, infinity) in which $\in$-induction fail?

I asked this question on Mathematics Stack Exchange here 4 days ago, to receive no answer yet, I thought this question already has a well known answer that is somehow evading me. Seeing that nobody answered thus far, makes me wonder if this is really an elementary issue? The whole issue is whether the proof that Foundation implies $\in$-induction necessitate existence of transitive closures for all sets, and since first order Zermelo doesn't prove the existence of transitive closures for all sets, then this raised this issue in my mind.