Synthetic aperture radar (SAR) satellites can provide microwave remote sensing images without weather and light constraints, so they are widely applied in the maritime monitoring field. Current SAR ship detection methods based on deep learning (DL) are difficult to deploy on satellites, because these methods usually have complex models and huge calculations. To solve this problem, based on the You Only Look Once version 5 (YOLOv5) algorithm, we propose a lightweight on-board SAR ship detector called Lite-YOLOv5, which (1) reduces the model volume; (2) decreases the floating-point operations (FLOPs); and (3) realizes the on-board ship detection without sacrificing accuracy. First, in order to obtain a lightweight network, we design a lightweight cross stage partial (L-CSP) module to reduce the amount of calculation and we apply network pruning for a more compact detector. Then, in order to ensure the excellent detection performance, we integrate a histogram-based pure backgrounds classification (HPBC) module, a shape distance clustering (SDC) module, a channel and spatial attention (CSA) module, and a hybrid spatial pyramid pooling (H-SPP) module to improve detection performance. To evaluate the on-board SAR ship detection ability of Lite-YOLOv5, we also transplant it to the embedded platform NVIDIA Jetson TX2. Experimental results on the Large-Scale SAR Ship Detection Dataset-v1.0 (LS-SSDD-v1.0) show that Lite-YOLOv5 can realize lightweight architecture with a 2.38 M model volume (14.18% of model size of YOLOv5), on-board ship detection with a low computation cost (26.59% of FLOPs of YOLOv5), and superior detection accuracy (1.51% F1 improvement compared with YOLOv5).