  Within the perturbative QCD approach and ignoring the contributions of long
distance and subleading penguin loops, we investigate $\bar B^0 \to D^0
\mu^+\mu^-$ decay in the large recoiling kinematic region in the Standard
Model. At the tree level, $\bar B^0$ decays to $D^0$ by exchanging a $W$ boson
accompanied by a virtual photon emission from the valence quarks of $\bar B^0$
and $D^0$ meson, then the virtual photon decays to the lepton pair.
Numerically, we find that the branching ratio decreases rapidly as the $q^2$
increases, and the branching ratio of $ \bar B^0\to D^0\mu^+\mu^-$ is
$(9.7_{-3.2}^{+4.2})\times 10^{-6}$ in the region $q^2 \in [1,5]
\mathrm{GeV}^2$. The order of the branching ratio shows a possibility to study
this interesting channel in the current $B$ factories and the Large Hadron
Collider. The precise experimental data will help us to test the factorization
approach and the QCD theory, in general.
