Tensor networks provide an efficient approximation of operations involving high dimensional tensors and have been extensively used in modelling quantum many-body systems. More recently, supervised learning has been attempted with tensor networks, primarily focused on tasks such as image classification. In this work, we propose a novel formulation of tensor networks for supervised image segmentation which allows them to operate on high resolution medical images. We use the matrix product state (MPS) tensor network on non-overlapping patches of a given input image to predict the segmentation mask by learning a pixel-wise linear classification rule in a high dimensional space. The proposed model is end-to-end trainable using backpropagation. It is implemented as a strided tensor network to reduce the parameter complexity. The performance of the proposed method is evaluated on two public medical imaging datasets and compared to relevant baselines. The evaluation shows that the strided tensor network yields competitive performance compared to CNN-based models while using fewer resources. Additionally, based on the experiments we discuss the feasibility of using fully linear models for segmentation tasks.(Source code: https://github.com/raghavian/strided-tenet )