The requirement for a niddah to immerse is a Torah level, D'oraita, law. However, it is not explicitly stated in any verse in Torah. This is an instance where the Rabbinic tradition is essential for a proper understanding of the Torah text.
There are a few different Torah sources given for the requirement that a woman in niddah immerse. These include VaYikra 15:18, which is understood by the Rambam as a 'binyan av', or archetype, for anyone who is tamei (ritually impure) needing to immerse. An alternative scriptural basis is VaYikra 15:21, which requires one who touches a niddah's bedding to immerse. Kal vachomer (a fortiori), a niddah herself must immerse. Another source is Bamidbar 31:23, in which a mikveh is referred to as "the waters of niddah." (For further reference, see Bet Yosef, Yoreh Deah 197:1.)
On another note, a zavah brings a sacrifice when she exits that status (VaYikra 15:25-30), but a niddah does not (VaYikra 15:19-24). Again, the Rabbinic tradition is important in understanding the verses.
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