In March 2021, an eruption began in the Fagradalsfjall volcanic system in Iceland after a quiescence of 6,000 years, which also marked the end of more than 800 years of dormancy in the Reykjanes Peninsula. In areas of volcanic activity, lava flow mapping and analysis play a significant role in monitoring and disaster risk management, because lava flows represent potential hazards to surrounding areas. This study used object-based image analysis (OBIA) and Sentinel-1 synthetic aperture radar (SAR) data to map the extent of the Fagradalsfjall lava flow and its evolution. We investigated two images, acquired on 18 May 2021 and 30 September 2021, syn- and post-eruption respectively. The calculated lava inundation area was 2.07 km² for 18 May 2021, and 5.03 km² post-eruption. The results of the application of the OBIA method on Sentinel-1 backscatter data reveal a high potential for lava flow mapping as they show high agreement with existing reference data (accuracies from 79% to 93%). However, the outcomes should be evaluated carefully because factors such as spatial resolution, SAR geometrical distortions and the OBIA segmentation process can influence the classification results.