Borrowed from Middle Low German nichte, from Old Saxon *nifta, from Proto-Germanic *niftiz.
This form replaced High German (obsolete) Niftel in the 17th century. It is based on the Low German shift -ft-→ -cht- (compare Gerücht); hence cognate with Old High German nift, nifta, Dutch nicht, English nift. Related to German Neffe (“nephew”). More at nift, neve.