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I'm pretty sure credit card companies are now required by law to have minimum payments that reflect at least *some* principle. Which means if you have a $0 due, that's not a minimum payment but reflects that you've already paid everything due up to the previous billing cycle and the new charges are not yet due (and thus are not yet earning interest). So no worries about being charged interest on that.
OP, assuming you're not carrying over a balance from a previous month and the pending amount due for next month is all new charges, you shouldn't pay anything when you're at $0 due unless you can pay *all* of it. If you have the money now, just save it as earmarked for that credit card payment when it comes due.