Hookworm disease is a major global public health concern, annually affecting 500-700 million of the world's poorest people. The World Health Organization is targeting the elimination of hookworm as a public health problem by 2030 using a strategy of mass drug administration (MDA) to at-risk human populations. However, in Southeast Asia and the Pacific the zoonotic hookworm species, Ancylostoma ceylanicum, is endemic in dogs and commonly infects people. This presents a potential impediment to the effectiveness of MDA that targets only humans. Here, we develop a novel multi-host (dog and human) transmission model of A. ceylanicum and compare the effectiveness of human-only and "One Health" (human plus dog) MDA strategies under a range of eco-epidemiological assumptions. We show that One Health interventions-targeting both dogs and humans-could suppress prevalence in humans to ≤ 1% by the end of 2030, even with only modest coverage (25-50%) of the animal reservoir. With increasing coverage, One Health interventions may even interrupt transmission. We discuss key unresolved questions on the eco-epidemiology of A. ceylanicum, the challenges of delivering MDA to animal reservoirs, and the growing importance of One Health interventions to human public health.