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Abstract Aim Theory predicts that the evolutionary adaptations of prey to reduce predator pressure often fail in confrontation with non‐native predators; thus, their predation usually leads to sharp declines of prey populations. However, over time, prey can develop anti‐predator adaptations, reduce predator impact and recover its population. We analyse the numerical response of multiple prey species to the impact of a non‐native predator on a large spatiotemporal scale. Location Poland. Methods Long‐term population dynamics of 13 waterbird species breeding in 123 sites were analysed with reference to the present and historical distribution of mink over 40 years. We rescaled the temporal waterbird dynamics to the time elapsed since the mink colonized each site. Results The steepest waterbird declines were recorded up to 15 years after establishment of the mink population, and in that period, waterbird abundance averaged across the 13 studied species declined by 50% but certain species showed different patterns: the abundance of eight species declined linearly or nonlinearly, whereas the breeding populations of five other species did not change significantly. Over time, the abundance of some declining species increased slightly and tended to stabilize at a lower level. The temporal pattern of waterbird dynamics averaged across species correlated closely with temporal changes of mink density with a 4‐year time‐lag. A projection of the observed patterns shows that waterbird decline following the expansion of mink has the shape of a wave travelling from the north to the south of Poland. Main conclusions We conclude that the impact of the invasive American mink should be considered an important factor affecting waterbird populations at a large geographical scale. The waterbird vulnerability to mink predation is species‐specific, and over time the negative impact grows weak as mink population densities decline.