The k-power domination number, gamma(P, k)(G), of a graph G is the minimum cardinality of a k-power dominating set of G. In this paper, we initiate the study of the k-power bondage number, b(P, k)(G), of a graph G, i.e., the minimum cardinality among all sets B subset of E(G) for which gamma(P, k)(G - B) >gamma(P, k)(G). We obtain a sharp upper bound for b(P, k)(G) in terms of the degree of G. We prove that b(P, k)(T) <= 2 for any nonempty tree T and also provide some conditions on T for b(P, k)(T) = 1.