Automatic ship segmentation from high-resolution Synthetic Aperture Radar (SAR) remote sensing images has been a topic of interest that has gradually gained attention over the years due to the abundance of earth observation sensors. Recently, deep learning methods have provided a breakthrough increasing the performance greatly by using large amount of labeled data. Yet, the high cost related to the samples labeling and their scarcity result in significant limitation of their wide use. Therefore, it is crucial to overcome the unlabeled inputs challenge and develop semi-supervised learning approaches to enhance the machine learning models capacity. Our letter proposes a semi-supervised segmentation algorithm for SAR images named SemiSegSAR based on the use of Graph Signal Processing. This method includes instance segmentation; texture and statistical SAR features to represent the nodes of the graph; K-nearest neighbors to construct the graph; and Sobolev minimization algorithm to tackle the problem of semi-supervised semantic segmentation. The proposed algorithm is trained and tested using the publicly available SSDD and HRSID ship detection datasets. Experiments show that SemiSegSAR outperforms the current state-of-the-art semi-supervised and supervised methods while requiring only few labeled data.