Ship detection is an important and challenging task in the field of synthetic aperture radar (SAR) image processing. Recently, deep learning technologies have yielded superior performance for object detection in remote sensing images. However, it is difficult to obtain the labels of SAR images, which limits the application of deep learning in ship detection from SAR images. To break the limitation of label information, we propose a self-supervised framework based on self-distillation for ship detection from SAR images in this paper. The framework consists of three core components: a self-supervised learning paradigm utilizing knowledge distillation, a deep residual shrinkage network (SAR-DRSN) model, and an oriented bounding boxes progressive generation model. The core of our method is a self-supervised variant of knowledge distillation, which propels the deep learning process in the absence of labeled data. The SAR-DRSN model excels in generating high-quality feature maps, significantly reducing the speckle noise. In addition, we introduce an iterative strategy for the accurate and precise delineation of ships, involving continuous refinement of oriented bounding boxes to optimize size and rotation angle for precise ship localization. Our experiments, obtained on two SAR datasets, demonstrate that the proposed method can achieve a satisfactory performance in ship detection without requiring any label information.