Abstract The spatial heterogeneity of vegetation greenness and potential aboveground biomass production for sheep farming has been assessed for Southwest Greenland. A Multi-Criteria Evaluation (MCE) model was set up to identify biophysical constraints on the present spatial distribution of farms and fields based on all existing sheep farms in a detailed study area. Time-integrated NDVI (TI-NDVI) from MODIS and observed temperatures (2000–2012) have been combined with a downscaled regional climate model (HIRHAM5) in order to establish a spatio-temporal model for future TI-NDVI, thus forecasting the dry biomass production available for sheep farming in steps of decades for the next 85 years. The model has been validated against observed biomass production and the present distribution of fields. Future biomass production is used to discuss the expansion of current farms and to identify new suitable areas for sheep farming. Interestingly, new suitable areas are located where sheep farms were situated during the Norse era more than 1000 years ago; areas which have been abandoned for the past 500 years. The study highlights the potential of establishing new areas for sheep farming in Arctic Greenland, where current and future climate changes are markedly amplified compared to global trends. However, for the study area the MCE model clearly indicates that the potential of expansion relies on contemporary infrastructural development.