Mapping of invasive alien plants (IAPs) is important for developing informed initiatives to assist environmentalists in managing the spread and impacts of IAPs. The Prosopis plant species is an aggressive IAP that has been considered a scourge in different regions of the globe. The aim of this study is to map the spatial distribution of the invasive alien Prosopis plant in southwestern Botswana using the higher spatial and spectral resolution Sentinel-2A (S2A) MultiSpectral Instrument (MSI) satellite sensor data. Supervised parametric maximum likelihood classification (MLC) was compared with the nonparametric Random Forest (RF) classifier for the detection and mapping of the Prosopis using 10 m S2A sensor bands, integrated with normalized difference vegetation index (NDVI) and Sentinel Improved Vegetation Index (SVI). Using S2A, S2A and NDVI, and S2A and SVI, MLC mapped the land use/land cover (LULC) in the study area with respective accuracies of 71.5%, 66.5%, and 79.9%, while RF mapped the LULC with accuracies of 93.2%, 77.3%, and 95.6%. Using RF, S2A multispectral data and the red edge wavelength-based SVI were found to be more suitable for mapping the distribution of Prosopis with classification accuracy of 18.3% higher than for NDVI. The study findings can be used by environmentalists, policy, and decision makers in the context of mapping, monitoring, and management of the invasive Prosopis.