Related to ī(“to turn sour”).[1] Could also be from māī itself from māhī. (This etymology is missing or incomplete. Please add to it, or discuss it at the Etymology scriptorium.)
Williams, Herbert William (1917) “moī”, in A Dictionary of the Maori Language, page 240
“moī” in John C. Moorfield, Te Aka: Maori–English, English–Maori Dictionary and Index, 3rd edition, Longman/Pearson Education New Zealand, 2011, →ISBN.