Accurate information on the extent and dynamics of ice cover is important at a global scale. Due to the day-night and weather independent imagery capabilities, Sentinel-1 (S1) is a reliable source for ice monitoring using Synthetic aperture radar (SAR) images. Therefore, this study focuses on an unsupervised method for extracting ice cover by exploiting dual-pol S1 SAR data. We adapt a constant false alarm rate (CFAR) detector for ice cover detection by examining the empirical distribution of a given metric over a water region, followed by a statistical comparison of the resulting distribution with the theoretical gamma distribution to derive the CFAR threshold value. To achieve ice detection, a binary image is first retrieved, and then the ice edges are quantified using the Canny edge detector. To evaluate the effectiveness of the proposed method, we applied it to SAR data from a challenging environment, including terrain, ice, and water. The results are further verified using Sentinel-2 (S2) as the ground truth data, which showed a maximum correlation in the extraction. Our findings demonstrate the soundness of the proposed method for iceberg extraction using Sentinel-1 data.