Acer monspessulanum (Montpellier Maple) is an important deciduous tree species native to the Mediterranean region. It is largely distributed in the southern part of western Europe; however, it is geographically less present in north Africa and western Asia. The effects of the most significant environmental variables for its habitat suitability, and climate change, are unclear in terms of the future changes to its distribution. The objective of the present study was to model the current and future geographical potential distribution of the Montpellier Maple in the Mediterranean basin and West Asia using maximum entropy modeling software (MaxEnt). The value of the Area Under the Curve (AUC) of MaxEnt was used to analyze the model’s performance. More than 5800 well-distributed presence points, elevation, slope, aspect, topographic wetness index (TWI), natural vegetation characteristics from MODIS products, and 19 bioclimatic variables were used to conduct the study. Regarding the projections of the species distribution under climate change, 17 global climatic models were used under two RCP scenarios (4.5 and 8.5) for the 2040–2060 and the 2060–2080 time periods. The results show that temperature seasonality (40% contribution to the model), elevation (33.5%), mean annual temperature (6.9%), mean annual precipitation (6.2%), and max temperature of the warmest month (4.5%) were identified as the primary factors that accounted for the current distribution of the Montpellier Maple. Under the climate change scenarios, MaxEnt predicts a large decrease in the species suitability area, with a shift towards the southwestern regions of the species distribution, especially to the mountainous zones of the Moroccan Atlas. Our results show that climate largely limits the distribution of the Montpellier Maple in the Mediterranean basin, as its change in the future is expected to significantly reduce the suitable area by more than 99% from the historical climate conditions, to reach only 16,166.9 and 9874.7 km² under the moderate RCP4.5 and extreme RCP8.5 scenarios, respectively, by the end of the 21st century. Our study can provide a good view of the future changes in the distribution of Montpellier Maple for its protection and sustainable management.