Predicting the distribution of alien species in areas not yet reached or where the species are still found in low abundance is crucial for implementing timely management strategies. Miconia calvescens has become one of the worst plant invaders in the Pacific including in the Society Islands (French Polynesia), the Hawaiian Islands, and tropical Australia. The species has been recently introduced to the Marquesas Islands (French Polynesia) where it started to spread. In this study, we aimed at predicting the potential distribution of Miconia across this archipelago. MAXENT modelling based on ~3,000 occurrence records from the native and introduced ranges of the species was used to predict its equilibrium distribution. Two types of environmental variables acting at different scales were considered: (1) climate variables at a 1 km scale for predicting the invasion risk over still Miconia-free Marquesan islands; and (2) topographic variables at a 10 m scale for refining prospections and guiding management strategies on the islands of Nuku Hiva and Fatu Hiva where Miconia currently occupies ~0.01% of the surface. Results differed substantially according to the origin of inputted occurrence records but models generally indicated that Miconia has the potential to spread over all inhabited Marquesan islands and over half of Nuku Hiva and a third of Fatu Hiva. Our approach provides valuable information for stakeholders to prevent future outbreaks. Without strong biosecurity measures, an early warning system, and appropriate control strategies in areas where it is already naturalized, Miconia could become a great threat to the outstanding biodiversity of the Marquesas Islands.