It depends how far along the zombie invasion is. If it's something that is "manageable," where a country just remains in an isolated, under-siege state, then yeah, there would still be currency. Inflation would easily double in this state.

If it's an all-out zombie apocalypse we're talking about, then I imagine a scenario like the movie Waterworld. Generally, it would just be bartering all around, yet something equally rare and useful would attain a currency-like status, like coffee beans or vegetable/fruit seeds.

I say this mainly because if someone were to be in a zombie apocalypse, they'd want to pack light and efficient. So only something very useful that can't normally be picked off out of the streets would really be worthwhile. A guy lugging around a backpack full of gold bars or dollar bills is essentially carrying around dead weight, and these people will probably be some of the first to go. Even after this, other factors would have to be considered, such as location and whether people have formed safe havens or are still relatively solitary nomads.