Massive gravity theories have been attracting a great deal of interest partly because graviton mass may give an alternative explanation for the accelerated expansion of the universe. We argue how to probe features of the massive gravity theories focusing on the observations of stochastic gravitational wave background generated in the inflationary era. We conduct the analysis based on a general quadratic action for those theories. As a result, we find that a universal feature is a sharp peak appearing in the gravitational wave spectrum, from which we may extract information on the graviton mass and also on the inflationary era. We also discuss the detectability of such a gravitational wave signal using the future-planned gravitational wave observatories.