The extinction of New Zealand's moa (Aves: Dinornithiformes) followed the arrival of humans in the late 13th century and was the final event of the prehistoric Late Quaternary megafauna extinctions. Determining the state of the moa populations in the pre-extinction period is fundamental to understanding the causes of the event. We sampled 281 moa individuals and combined radiocarbon dating with ancient DNA analyses to help resolve the extinction debate and gain insights into moa biology. The samples, which were predominantly from the last 4,000 years preceding the extinction, represent four sympatric moa species excavated from five adjacent fossil deposits. We characterized the moa assemblage using mitochondrial DNA and nuclear microsatellite markers developed specifically for moa. Although genetic diversity differed significantly among the four species, we found that the millennia preceding the extinction were characterized by a remarkable degree of genetic stability in all species, with no loss of heterozygosity and no shifts in allele frequencies over time. The extinction event itself was too rapid to be manifested in the moa gene pools. Contradicting previous claims of a decline in moa before Polynesian settlement in New Zealand, our findings indicate that the populations were large and stable before suddenly disappearing. This interpretation is supported by approximate Bayesian computation analyses. Our analyses consolidate the disappearance of moa as the most rapid, human-facilitated megafauna extinction documented to date.