  We report on a search for the flavor-changing neutral current decay $D^0 \to
\mu^+\mu^-$ using $50 \times 10^6$ events recorded with a dimuon trigger in
interactions of 920 GeV protons with nuclei by the HERA-B experiment. We find
no evidence for such decays and set a 90% confidence level upper limit on the
branching fraction $Br(D^0 \to \mu^+\mu^-) <2.0 \times 10^{-6}$.
