Dedicated underground experiments searching for dark matter have little sensitivity to GeV and sub-GeV masses of dark matter particles. We show that the decay of B mesons to K(K(*)) and missing energy in the final state can be an efficient probe of dark matter models in this mass range. We analyze the minimal scalar dark matter model to show that the width of the decay mode with two dark matter scalars B-->KSS may exceed the decay width in the standard model channel, B-->Knunu , by up to 2 orders of magnitude. Existing data from B physics experiments almost entirely exclude dark matter scalars with masses less than 1 GeV. Expected data from B factories probe the range of dark matter masses up to 2 GeV.