A significant amount of the produced solid waste reaching the oceans is made of plastics. The amount of plastic debris in the ocean and coastal areas is steadily increasing and is now a major global environmental issue. The monitoring of marine plastic litter, ground-based monitoring systems and/or field campaigns are time-consuming, expensive, require great organisational efforts, and provide very limited information in terms of the spatial and temporal dynamics of marine debris. Earth Observation (EO) by satellite can contribute significantly to marine plastic litter detection. In 2019, a new hyperspectral satellite, called PRISMA, was launched by the Italian Space Agency. The high spectral resolution of PRISMA may allow for better detection of floating plastic materials. At the same time, Machine Learning (ML) algorithms have the potential to find hidden patterns and identify complex relations among data and are increasingly employed in EO. This paper presents the development of a new method of identifying floating plastic objects in coastal areas by exploiting pan-sharpened hyperspectral PRISMA data, based on the combination of unsupervised and supervised ML algorithms. The study consisted of a configuration phase, during which the algorithms were trained in a fully controlled test, and a validation phase, in which the pre-trained algorithms were applied to satellite data collected at different sites and in different periods of the year. Despite the limited input data, results suggest that the tested ML approach, applied to pan-sharpened PRISMA data, can effectively recognise floating objects and plastic targets. The study indicates that increasing input datasets can help achieve higher-quality results.