My initial thought was along the lines of 'but Maori are just part of the community' - but while that's true, there are still some options that are actually pretty awesome. And to time with the Rugby World Cup, Qualmark now has a Marae Stay Experience rating - maraes being traditional community ancestral house or meeting venue.
There are some good options out there, and I'll list a couple of them now:
Ngati Whare marae retreats - two marae on site, where you get two nights stay (at least), cultural experiences, guided tours of the valley and surrounding forest, and an opportunity to see some of their arts and culture.
Auckland Maori Culture Tours - probably touristy, but the contents look like you really get the complete experience. From the initial Hongi (nose touch), you'll learn some language, go to a great marae, sleep over in a traditional meeting house (optional, you can stay elsewhere for extra, but why would you!), great Maori food - and importantly, you'll share in making a Hangi - the traditional earth oven meal (has to be seen and tasted to appreciate!), learn about the Haka and try some of the traditional arts - weaving, carving, as well as learn about the history and culture.
If I were a tourist in NZ, the latter one really would cover everything, although as a warning - like so many things in this vein, it's probably a little touristy.
Of course, the other option is to try couchsurfing and see if you can find a homestay on that! However it'd be more likely to be modern rather than traditional culture, of course.