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Induced seismicity is one of the negative phenomena caused by anthropogenic activities that include mining of minerals. This phenomenon manifests itself as sudden and unpredictable shocks of rock mass, which can cause surface deformation and damage to ground infrastructure. Until the advent of satellite radar interferometry that enables analysis of historical events, the characteristics of these unexpected surface deformations were difficult to assess. The main aim of the research was the spatial analysis of the geometry of surface displacements caused by eight induced tremors in the Rudna copper mine (SW Poland) and the dependence of deformation characteristics (vertical displacements, extent) on the induced shock energy. For this purpose, Sentinel-1 satellite imagery, the differential radar satellite interferometry (DInSAR) method and geographic information systems (GIS) based spatial statistics were used. Vertical displacements were mapped on the basis of 37 calculated interferograms. Spatial statistics on the pixel-to-pixel level were performed in the GIS Map Algebra environment. In the result, descriptive and spatial statistics characterizing deformations caused by individual shocks were calculated. The average values of vertical displacements ranged from −44 to −119 mm. Strong, statistical correlation between the extent, maximum vertical displacement, and energy values was determined. In addition, geometries of the formed deformation areas were analyzed and presented graphically. The results obtained in this research constitute development of a knowledge base on surface displacements caused by induced tremors in underground copper mining.