Accurate segmentation of medical images is crucial for diagnostic purposes, including cell segmentation, tumor identification, and organ localization. Traditional convolutional neural network (CNN)-based approaches struggled to achieve precise segmentation results due to their limited receptive fields, particularly in cases involving multi-organ segmentation with varying shapes and sizes. The transformer-based approaches address this limitation by leveraging the global receptive field, but they often face challenges in capturing local information required for pixel-precise segmentation. In this work, we introduce DwinFormer, a hierarchical encoder-decoder architecture for medical image segmentation comprising a directional window (Dwin) attention and global self-attention (GSA) for feature encoding. The focus of our design is the introduction of Dwin block within DwinFormer that effectively captures local and global information along the horizontal, vertical, and depthwise directions of the input feature map by separately performing attention in each of these directional volumes. To this end, our Dwin block introduces a nested Dwin attention (NDA) that progressively increases the receptive field in horizontal, vertical, and depthwise directions and a convolutional Dwin attention (CDA) that captures local contextual information for the attention computation. While the proposed Dwin block captures local and global dependencies at the first two high-resolution stages of DwinFormer, the GSA block encodes global dependencies at the last two lower-resolution stages. Experiments over the challenging 3D Synapse Multi-organ dataset and Cell HMS dataset demonstrate the benefits of our DwinFormer over the state-of-the-art approaches. Our source code will be publicly available at \url{https://github.com/Daniyanaj/DWINFORMER}.