A new mechanism has been proposed to simultaneously explain the presence of dark matter and the matter-antimatter asymmetry in the Universe. This scenario predicts exotic B-meson decays into a baryon and a dark-sector antibaryon (ψD) with branching fractions accessible at B factories. We present a search for B→ΛψD decays using data collected by the BABAR experiment at SLAC. This reaction is identified by fully reconstructing the accompanying B meson and requiring the presence of a single Λ baryon in the remaining particles. No significant signal is observed, and bounds on the B→ΛψD branching fraction are derived in the range 0.13–5.2×10−5 for 1.0<4.2 GeV/c2. These results set strong constraints on the parameter space allowed by the theory.