We consider Markovian open quantum dynamics (MOQD) in the continuum. We show that, up to small-probability tails, the supports of quantum states evolving under such dynamics propagate with finite speed in any finite-energy subspace. More precisely, we prove that if the initial quantum state is localized in space, then any finite-energy part of the solution of the von Neumann–Lindblad equation is approximately localized inside an energy-dependent light cone. We also obtain an explicit upper bound for the slope of this light cone.