It has been proposed by Goldberg and Hall that the dark matter in galactic halos may be a type of shadow matter which interacts electromagnetically with ordinary matter (via a mixing effect) with effective charge ||Q||=2ɛe where ɛ<<1. We put constraints on the mass (ms) and effective charge (i.e., ɛ) of such particles by examining their possible production and detection in high-statistics proton beam-dump experiments. We find, for example, that ɛ<~2×10-2 for 1<~ms<~200 MeV.