Climate change‐amplified temperature anomalies pose an imminent threat to coral reef ecosystems. While much focus has been placed on the effects of heat stress on scleractinian corals—including bleaching, mortality, and loss of reef structural complexity—and many studies have documented changes to reef fish communities arising indirectly from shifts in benthic composition, the direct impacts of heat stress on reef fish are much less well understood. Here, we quantify the direct and indirect effects of heat stress on reef fishes, using underwater visual censuses of coral reef fish communities conducted before, during, and after the 2015–2016 El Niño‐induced global coral bleaching event. Surveys took place at the epicenter of this event, at 16 sites on Kiritimati (Republic of Kiribati; central equatorial Pacific) spanning across a gradient of local human disturbance. We expected that heat stress would have both direct and indirect negative effects on the reef fish community, with direct effects resulting from physiological stress during the event and indirect effects manifesting afterward as a consequence of coral mortality, and that the ability of fish communities to recover following the heat stress would depend on levels of local human disturbance. We found that total reef fish biomass and abundance declined by >50% during heat stress, likely as a result of vertical migration of fish to cooler waters. One year after the cessation of heat stress, however, total biomass, abundance, and species richness had recovered to, or even exceeded, pre‐heat stress levels. However, the biomass of corallivores declined by over 70% following severe coral loss, and reefs exposed to higher levels of local human disturbance showed impaired recovery following the heat stress. These findings enhance understanding of the projected impacts of climate change‐associated marine heatwaves on reef fishes, and highlight the interacting effects of local and global stressors on this vital component of coral reef ecosystems.