Interspecific hybridization is recognized as an important process in the evolutionary dynamics of both speciation and the reversal of speciation. However, our understanding of the spatial and temporal patterns of hybridization that erode versus promote species boundaries is incomplete. The endangered, endemic koloa maoli (or Hawaiian duck, Anas wyvilliana) is thought to be threatened with genetic extinction through ongoing hybridization with an introduced congener, the feral mallard (A. platyrhynchos). We investigated spatial and temporal variation in hybrid prevalence in populations throughout the main Hawaiian Islands, using genomic data to characterize population structure of koloa, quantify the extent of hybridization, and compare hybrid proportions over time. To accomplish this, we genotyped 3,308 double‐digest restriction‐site‐associated DNA (ddRAD) loci in 425 putative koloa, mallards, and hybrids from populations across the main Hawaiian Islands. We found that despite a population decline in the last century, koloa genetic diversity is high. There were few hybrids on the island of Kauaʻi, home to the largest population of koloa. By contrast, we report that sampled populations outside of Kauaʻi can now be characterized as hybrid swarms, in that all individuals sampled were of mixed koloa × mallard ancestry. Further, there is some evidence that these swarms are stable over time. These findings demonstrate spatial variation in the extent and consequences of interspecific hybridization, and highlight how islands or island‐like systems with small population sizes may be especially prone to genetic extinction when met with a congener that is not reproductively isolated.