In this paper, the finite-time stability (FTS) of switched Boolean networks (SBNs) with Markov jump disturbances under the conditions of arbitrary switching signals is studied. By using the tool of the semi-tensor product, the equivalent linear-like form of SBNs with Markov jump disturbances is first established. Next, to facilitate investigation, we convert the addressed system into an augmented Markov jump Boolean network (MJBN), and propose the definition of the switching set reachability of MJBNs. A necessary and sufficient criterion is developed for the FTS of SBNs with Markov jump disturbances under the conditions of arbitrary switching signals. Finally, we give two examples to illustrate the effectiveness of our work.