  New and complimentary constraints are placed on the spin-independent
interactions of dark matter with baryonic matter. Similar to the Earth and
other planets, the Moon does not have any major internal heat source. We derive
constraints by comparing the rate of energy deposit by dark matter
annihilations in the Moon to 12 mW/m$^2$ as measured by the Apollo mission. For
light dark matter of mass $\mathcal{O}(10)$ GeV, we also examine the
possibility of dark matter annihilations in the Moon limb. In this case, we
place constraints by comparing the photon flux from such annihilations to that
of the Fermi-LAT measurement of $10^{-4}$ MeV/cm$^2$s. This analysis excludes
spin independent cross section $\gtrsim 10^{-37}$ $\rm{cm}^2$ for dark matter
mass between 30 and 50 GeV.
