Abstract Globally, freshwater fishes are among the taxa most vulnerable to climate change but are generally understudied in tropical island ecosystems where climate change is predicted to alter the intensity, frequency and duration of extreme flow events. These changes may impact stream ecosystems and native and non‐native biota in complex ways. We compiled an extensive dataset of fish assemblages collected at 119 sites across the Caribbean island of Puerto Rico from 2005 to 2015. We coupled these data with stream flow indices and dam height to understand associations between flow and fish assemblage structure. Sixteen percent of sites contained exclusively non‐native species, 34% contained exclusively native species, and 50% contained native and non‐native species. We built generalised linear models and conducted all subsets model selection to identify extreme flow variables explaining variation in native and non‐native species richness and biomass. We also built models to determine the combined effects of extreme flows and the presence of non‐native species on native species richness and biomass. Extreme flows and dam height were important in explaining variations in native and non‐native species richness and biomass. Model averages showed native biomass decreased by 0.42 kg/ha with a 1‐m increase in dam height, by 0.05 kg/ha with 1 cm/s increase in maximum mean daily high flow and by 3.45 kg/ha with each additional day increase in maximum high flow duration, and increased by 2.06 kg/ha with each additional day increase in mean high flow duration. Model averages predicted that non‐native biomass increased by 1.32 kg/ha with a 1‐m increase in dam height and by 0.01 kg/ha with each additional day increase in mean high flow duration, and decreased by 0.36 kg/ha with each additional day increase in maximum high flow duration. Model averages also predicted an increase in native and non‐native biomass of 0.71 gage and 0.06 kg/ha, respectively, with each additional day increase in maximum low flow duration. The combined effects of non‐native species presence and extreme flows changed the relationship between maximum high and low flow durations and native biomass. Model averages showed that native biomass increased by 1.83 kg/ha with each additional day increase in maximum high flow duration and decreased by 2.52 kg/ha with each additional day increase in maximum low flow duration when non‐native species were present. Native fishes may be able to better cope with longer maximum durations of low flows than expected when non‐native fishes are absent. In mixed fish assemblages, extended maximum durations of high flows may act as a control of non‐native species and dampen their negative effect on native species, but longer maximum durations of low flows may heighten the negative effects of non‐native fishes. Our results are informative for tropical island ecosystems globally and can guide the management and conservation of native fishes, particularly when faced with the dual threats of climate change and non‐native species. Managers may consider increasing efforts to conserve native fishes in Caribbean rivers by maintaining connectivity and habitat complexity while preventing non‐native species introductions.