Compound of kami +‎ na (な, Old Japanese possessive particle, apophonic form of の (no)) +‎ tsuki (月 'month').

The use of the kanji 無 'not, none' for the na portion is an example of phonetic ateji (当て字). In one folk etymology, kami were said to assemble at 出雲大社 (Izumo Taisha, “Izumo Grand Shrine”) at this month, leaving no gods in the rest of Japan.