As in most fields, you'll find once you dive in that the title "NLP" covers a fairly broad range of sub-fields. The math requirements vary widely depending on what you're trying to accomplish. So a little more detail about your goals would help.
That said, I can address parsing and the related fields I have some experience in, and offer very general comments on a few others.
You'll find discrete math and automata theory useful in any computer science discipline, so you can't go wrong there.
Some NLP work is closer to linguistics or psychology than computer science. So some linguistic theory might be helpful if that's where your interests lie, and some background in statistical hypothesis testing (applied statistics of the sort you might find in a social science department, although the more rigorous the better).
For morphology, tagging, parsing, and related fields, some probability theory is helpful (as is experience thinking about dynamic programming, although that's not really math background). If you're doing anything involving machine learning (which is most of NLP), it helps to understand some linear algebra.
That said, if your goals are more applied, you can accomplish quite a lot by applying existing tools, without detailed knowledge of the underlying math (it doesn't require any linear algebra to train an SVM, if all you need is a classifier).