The German equivalent would be p. Adr. (although I haver never seen that much in the wild). z. Hd. is used in the opposite way, i.e. you write the actual recipient after it, not the address provider.
Ah yes, that was stupid of me. Although it can be used pretty much the same. "A c/o B" is in practice not much different from "B z.Hd. A", although it's legally different (when it comes to who is authorized to accept the mail if a signature is needed etc.).
I haven't actually seen "p. Adr." ever in my life.
[edit – wrong:] The German-language equivalent (that most young people won't even recognize anymore) is "z. Hd." ("zu Händen" – "to the hands of").