The detection and repairment of methane leaks from fossil fuel production activities have been identified as a key climate change mitigation strategy. Several types of optical satellite sensors have recently shown potential to support this task. Spaceborne imaging spectrometers measuring in the 400–2500 nm spectral range belong to this group. These instruments measure the solar radiation reflected by the Earth in hundreds of spectral channels with a typical spectral resolution of 10 nm and a spatial resolution of 30 m. The PRISMA mission from the Italian Space Agency is the first system of this type providing data openly to the international scientific community. In this work, we evaluate the potential of PRISMA to map methane point emissions, which are typical for fossil fuel production activities. Our retrieval of methane concentration enhancements is based on a matched-filter based algorithm applied to PRISMA spectra in the 2300 nm shortwave infrared spectral region. We perform a simulation-based sensitivity analysis to assess the retrieval performance for different sites. We find that surface brightness and homogeneity are major drivers for the detection and quantification of methane plumes with PRISMA, with retrieval precision errors ranging from 61 to 197 parts-per-billion in the evaluated images. The potential of PRISMA for methane mapping is further illustrated by real plume detections at different methane hotspot regions, including oil and gas extraction fields in Algeria, Turkmenistan, and the USA (Permian Basin), and coal mines in the Shanxi region in China. Our study reports several important findings regarding the potential and limitations of PRISMA for methane mapping, most of which can be extrapolated to upcoming satellite imaging spectroscopy missions.