The Earth-Moon system has unique chemical and isotopic signatures compared with other planetary bodies; any successful model for the origin of this system therefore has to satisfy these chemical and isotopic constraints. The Moon is substantially depleted in volatile elements such as potassium compared with the Earth and the bulk solar composition, and it has long been thought to be the result of a catastrophic Moon-forming giant impact event. Volatile-element-depleted bodies such as the Moon were expected to be enriched in heavy potassium isotopes during the loss of volatiles; however such enrichment was never found. Here we report new high-precision potassium isotope data for the Earth, the Moon and chondritic meteorites. We found that the lunar rocks are significantly (>2σ) enriched in the heavy isotopes of potassium compared to the Earth and chondrites (by around 0.4 parts per thousand). The enrichment of the heavy isotope of potassium in lunar rocks compared with those of the Earth and chondrites can be best explained as the result of the incomplete condensation of a bulk silicate Earth vapour at an ambient pressure that is higher than 10 bar. We used these coupled constraints of the chemical loss and isotopic fractionation of K to compare two recent dynamic models that were used to explain the identical non-mass-dependent isotope composition of the Earth and the Moon. Our K isotope result is inconsistent with the low-energy disk equilibration model, but supports the high-energy, high-angular-momentum giant impact model for the origin of the Moon. High-precision potassium isotope data can also be used as a ‘palaeo-barometer’ to reveal the physical conditions during the Moon-forming event.