In this paper, we explore the possibility of detecting polar lows in C-band SAR images by means of deep learning. Specifically, we introduce a novel dataset consisting of Sentinel-1 images labeled as positive; representing a maritime mesocyclone, or negative; representing a normal sea state. The dataset is constructed using the ERA5 dataset as baseline and it consists of 2004 annotated images. To our knowledge, this is the first dataset of its kind to be publicly released. The dataset is used to train a deep learning model to classify the labeled images. Evaluated on an independent test set, the model yields an F-1 score of 0.95, indicating that polar lows can be consistently detected from SAR images. Interpretability techniques applied to the deep learning model reveal that atmospheric fronts and cyclonic eyes are key features in the classification. Moreover, experimental results show that the model is accurate even if: (i) such features are significantly cropped due to the limited swath width of the SAR, (ii) the features are partly covered by sea ice and (iii) land is covering significant parts of the images. By evaluating the model performance on multiple input image resolutions (pixel sizes of 500m, 1km and 2km), it is found that higher resolution yield the best performance. This emphasises the potential of using high resolution sensors like SAR for detecting polar lows, as compared to conventionally used sensors such as scatterometers.