Despite investments in disaster resilience, flooding continues to disrupt healthcare systems, both by limiting access and through failures in the surrounding transportation network. Existing models for mitigation planning often overlook critical dynamics, such as traffic rerouting, particularly at the national scales necessary for effective planning. Here we present a scalable method to identify hospitals at risk of emergency response delays and service disruptions caused by flood-induced traffic impacts. Our approach integrates a regional flood model with a gravity-based traffic model to simulate traffic flow from open-source road data. Our findings reveal hidden risks for hospitals located far from flood zones, showing how flood-related road disruptions and traffic rerouting can reduce access to critical healthcare services. In particular, we found 75 (of 2,475) hospitals at risk of patient surges beyond their regular capacity, driven solely by flood-related traffic disruptions. Of these, a third are more than 10 km from the nearest inundation, suggesting these facilities may be unaware and thus under-prepared — risks that have, until now, remained hidden from assessments.