Natural and anthropogenic disasters can cause significant damage to urban infrastructure, landscape, and loss of human life. Satellite based remote sensing plays a key role in rapid damage assessment, post-disaster reconnaissance and recovery. In this study, we aim to assess the performance of Sentinel-1 and Sentinel-2 data for building damage assessment in Kyiv, the capital city of Ukraine, due to the ongoing war with Russia. For damage assessment, we employ a simple and robust SAR log ratio of intensity for the Sentinel-1, and a texture analysis for the Sentinel-2. To suppress changes from other features and landcover types not related to urban areas, we construct a mask of the built-up area using the OpenStreetMap building footprints and World Settlement Footprint (WSF), respectively. As it is difficult to get ground truth data in the ongoing war zone, a qualitative accuracy assessment with the very high-resolution optical images and a quantitative assessment with the United Nations Satellite Center (UNOSAT) damage assessment map was conducted. The results indicated that the damaged buildings are mainly concentrated in the northwestern part of the study area, wherein Irpin, and the neighboring towns of Bucha and Hostomel are located. The detected building damages show a good match with the reference WorldView images. Compared with the damage assessment map by UNOSAT, 58% of the damaged buildings were correctly classified. The results of this study highlight the potential offered by publicly available medium resolution satellite imagery for rapid mapping damage to provide initial reference data immediately after a disaster.