Isotopic compositions of reservoirs in the Moon can be constrained from analysis of rocks generated during lunar magmatic differentiation. Mare basalts sample the largest lunar mantle volume, from olivine- and pyroxene-rich cumulates, whereas ferroan anorthosites and magnesian-suite rocks represent early crustal materials. Incompatible element enriched rocks, known as ‘KREEP,’ probably preserve evidence for the last highly differentiated melts. Here we show that mare basalts, including Apollo samples and meteorites, have remarkably consistent δ⁶⁶Zn values (+1.4±0.2‰) and Zn abundances (1.5 ± 0.4 ppm). Analyses of magnesian-suite rocks show them to be characterized by even heavier δ⁶⁶Zn values (2.5 to 9.3‰) and low Zn concentrations. KREEP-rich impact melt breccia Sayh al Uhaymir 169 has a nearly identical Zn composition to mare basalts (δ⁶⁶Zn=1.3‰) and a low Zn abundance (0.5 ppm). Much of this variation can be explained through progressive depletion of Zn and preferential loss of the light isotopes in response to evaporative fractionation processes during a lunar magma ocean. Samples with isotopically light Zn can be explained by either direct condensation or mixing and contamination processes at the lunar surface. The δ⁶⁶Zn of Sayh al Uhaymir 169 is probably compromised by mixing processes of KREEP with mafic components. Correlations of Zn with Cl isotopes suggest that the urKREEP reservoir should be isotopically heavy with respect to Zn, like magnesian-suite rocks. Current models to explain how and when Zn and other volatile elements were lost from the Moon include nebular processes, prior to lunar formation, and planetary processes, either during giant impact, or magmatic differentiation. Our results provide unambiguous evidence for the latter process. Notwithstanding, with the currently available volatile stable isotope datasets, it is difficult to discount if the Moon lost its volatiles relative to Earth either during giant impact or exclusively from later magmatic differentiation. If the Moon did begin initially volatile-depleted, then the mare basalt δ⁶⁶Zn value likely preserves the signature, and the Moon lost 96% of its Zn inventory relative to Earth and was also characterized by isotopically heavy Cl (δ³⁷Cl=≥8‰). Alternative loss mechanisms, including erosive impact removing a steam atmosphere need to be examined in detail, but nebular processes of volatile loss do not appear necessary to explain lunar and terrestrial volatile inventories.