  Based on a vanishing theorem for non-fibered knots due to Friedl and Vidussi,
we define the twisted Alexander vanishing order of a knot to be the order of
the smallest finite group such that the corresponding twisted Alexander
polynomial is zero. In this paper, we show its basic properties, and provide
several explicit values for knots with $10$ or fewer crossings. Moreover, we
characterize a finite group admitting the zero-twisted Alexander polynomial.
