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Optimal mean-square error estimators of systems with interrupted measurements are infinite dimensional, because these systems belong to the class of hybrid systems. This renders the calculation of a lower bound for the estimation error of the interruption process in these systems of particular interest. Recently it has been shown that a Crame´r-Rao-type lower bound on the interruption process estimation error is trivially zero. In the present work, a nonzero lower bound for a class of systems with Markovian interruption variables is proposed. Derivable using the well-known Weiss-Weinstein bound, this lower bound can be easily evaluated using a simple recursive algorithm. The proposed lower bound is shown to depend on a measure of the interruption chain transitional determinism, the measurement noise sensitivity to interruption process switchings, and a measure of the system's state estimability. In some cases, identified in this correspondence, the proposed bound is tight. The use of the lower bound is illustrated via a simple numerical example.