The Rambam famously defines chuppah as yichud – “yichud zeh hu hanikra knisa l’chuppah v’hu hanikra nisu’in” (Ishus 10:1) – and requires that a women be “re’uya l’biya” for marriage to take effect, to the exclusion of a nidah. The Rishonim point to two gemaras as possible sources for the Rambam's opinion:
1) Kesubos 56a discusses whether a women who had chuppas nidah is koneh tosefes kesubah despite the fact that the marriage is unconsumated. Does this mean that chupas nidah is not a full marriage? The many Rishonim who disagree with the Rambam understand the gemara to simply be saying that an unconsumated marriage is insufficient reason for the women to collect the money the husband added to the kesubah specifically for the sake of marriage. The very fact that the gemara raises the issue only in the context of tosefes kesubah and not as a general question of whether chupas nidah is koneh would seem to underscore their point.
2) Kesubos 2a debates whether a women has a right to mezonos (support) if due to some ones, such as nidah, the wedding date has to be postponed. The Rishonim again reject this proof - the gemara does not mean that chupas nidah is invalid, but simply that it constitutes a valid ones claim if the parties do not wish to go ahead with a chuppah on that date.
The great difficulty in the Rambam raised by the Ran is that chuppah works for psulos (Yevamos 57), women who are forbidden to their partner because of an issur lav, so why should it not work for niddah as well? What is more troubling is that the Rambam seems internally inconsistant. The statement that chupah is yichud and that is what defines marriage seems contradicted by a gemara we discussed previously. Kesubos 48 writes that once a father gives his daughter to her husband or his emissaries, she is legally his wife. The Rambam himself paskens that after this mesira has occurred the husband has the right to inherit (Rambam Ishus 22:1-2) and to absolve his wife's nedarim (Rambam Nedarim 11:22). Why then is a chupas nidah invalid? Even if the husband cannot have relations with his wife, it should be no worse than if a father hands his daughter over to the husband's emissaries?