We report on the first Belle search for a light CP-odd Higgs boson, $A^{0}$, that decays into low mass dark matter, $chi$, in final states with a single photon and missing energy. We search for events produced via the dipion transition $Upsilon(textrm{2S})rightarrowUpsilon(textrm{1S})pi^{+}pi^{-}$, followed by the on-shell process $Upsilon(textrm{1S})rightarrowgamma A^{0}$ with $A^{0} rightarrowchichi$, or by the off-shell process $Upsilon(textrm{1S})rightarrowgammachichi$. Utilizing a data sample of 157.3 $times$ 10$^{6}$ $Upsilon(textrm{2S})$ 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 $textrm{GeV/}textit{c}^{2}$ and $M_{chi} <$ 4.44 $textrm{GeV/}textit{c}^{2}$. 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 $textrm{GeV/}textit{c}^{2}$.
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