We report on the first Belle search for a light CP-odd Higgs boson, A^{0}, that decays into low mass dark matter, χ, in final states with a single photon and missing energy. We search for events produced via the dipion transition ϒ(2S)→ϒ(1S)π^{+}π^{-}, followed by the on-shell process ϒ(1S)→γA^{0} with A^{0}→χχ, or by the off-shell process ϒ(1S)→γχχ. Utilizing a data sample of 157.3×10^{6} ϒ(2S) decays, we find no evidence for a signal. We set limits on the branching fractions of such processes in the mass ranges M_{A^{0}}<8.97 GeV/c^{2} and M_{χ}<4.44 GeV/c^{2}. We then use the limits on the off-shell process to set competitive limits on WIMP-nucleon scattering in the WIMP mass range below 5 GeV/c^{2}.