To detect deforestation using Earth Observation (EO) data, widely used methods are based on the detection of temporal changes in the EO measurements within the deforested patches. In this paper, we introduce a new indicator of deforestation obtained from synthetic aperture radar (SAR) images, which relies on a geometric artifact that appears when deforestation happens, in the form of a shadow at the border of the deforested patch. The conditions for the appearance of these shadows are analyzed, as well as the methods that can be employed to exploit them to detect deforestation. The approach involves two steps: (1) detection of new shadows; (2) reconstruction of the deforested patch around the shadows. The launch of Sentinel-1 in 2014 has opened up opportunities for a potential exploitation of this approach in large-scale applications. A deforestation detection method based on this approach was tested in a 600,000 ha site in Peru. A detection rate of more than 95% is obtained for samples larger than 0.4 ha, and the method was found to perform better than the optical-based UMD-GLAD Forest Alert dataset both in terms of spatial and temporal detection. Further work needed to exploit this approach at operational levels is discussed.