Constraints on Dark Matter from the Moon

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.