The use of bioclimatic models to predict areas subject to invasion by exotic species has been important in the development of preventive conservation measures. The native New Zealand mudsnail Potamopyrgus antipodarum is an invasive mollusc, now with a worldwide distribution, that causes economic and ecological problems in invaded areas and has recently been designated as one of the 100 worst invasive species in Europe. In this study we sought to determine the potential distribution of and areas susceptible to invasion by P. antipodarum in South America and worldwide, in present and future scenarios (2070), using MaxEnt models. The models were developed using georeferenced occurrence data and bioclimate and hydroclimate variables to predict scenarios of the geographical distribution of P. antipodarum. Possible routes of invasion into South America were predicted. Present‐day scenario of the worldwide distribution (all known occurrences) of P. antipodarum, based on the bioclimatic and hydroclimatic models, are highly accurate, with area under curve higher than of 0.87. The models indicated that environmentally suitable areas exist in South America and in other regions of the world where the species has not yet been recorded. The predicted susceptibility includes approximately 80 protected areas in the South American continent. Models projected in an optimistic and pessimistic future scenario, based on the worldwide distribution, show increased environmental suitability of regions outside the current species distribution, including Brazil (south‐west), Uruguay (near Mirim Lagoon), Nigeria, Ethiopia (lakes Tana and Chomen), Tanzania, Cameroon (bordering lakes Bamendjing, Bankim, and Mbakaou), Equatorial Guinea, Congo, Rwanda, Burundi (Lake Tanganyika environs), Uganda, Tanzania (Naivasha), and South Africa (surrounding Gordon's Bay). The main vector for dispersal to South America would be ballast water coming from waterways and ports located in the predicted areas. Fish farming is also a possible route, since the mudsnail is resistant to the digestive tract of rainbow trout (Oncorhynchus mykiss). Current records and predicted susceptible areas coincide with port areas and sites where this fish is farmed. Geographical distribution modelling proved to be helpful in identifying environmentally suitable areas for the invasion of P. antipodarum. The model also suggests a future expansion of the species distribution, possibly affected by climate change.