Climate models predict increases in drought conditions in many parts of the tropics. Yet the response of tropical forests to drought remains highly uncertain, especially with regards to the factors that generate spatial heterogeneity in drought response across landscapes. In this study, we used Landsat imagery to assess the impacts of a severe drought in 2015 across an ~80,000‐ha landscape in Puerto Rico. Specifically, we asked whether drought effects varied systematically with topography and with forest age, height, and fragmentation. We quantified drought impacts using anomalies of two vegetation indices, the enhanced vegetation index (EVI) and normalized difference water index (NDWI), and fit random forest models of these metrics including slope, aspect, forest age, canopy height, and two indices of fragmentation as predictors. Drought effects were more severe on drier topographic positions, that is, steeper slopes and southwest‐facing aspects, and in second‐growth forests. Shorter and more fragmented forests were also more strongly affected by drought. We also assessed which factors were associated with stronger recovery from drought. Factors associated with more negative drought anomalies were also associated with more positive postdrought anomalies, suggesting that increased light availability as a result of drought led to high rates of recovery in forests more severely affected by drought. In general, recovery from drought was rapid across the landscape, with postdrought anomalies at or above average across the study area. This suggests that forests in Puerto Rico might be resilient to a single‐year drought, though vulnerability to drought varies depending on forest characteristics and landscape position.