Semantic segmentation involves classifying each pixel into one of a pre-defined set of object/stuff classes. Such a fine-grained detection and localization of objects in the scene is challenging by itself. The complexity increases manifold in the presence of blur. With cameras becoming increasingly light-weight and compact, blur caused by motion during capture time has become unavoidable. Most research has focused on improving segmentation performance for sharp clean images and the few works that deal with degradations, consider motion-blur as one of many generic degradations. In this work, we focus exclusively on motion-blur and attempt to achieve robustness for semantic segmentation in its presence. Based on the observation that segmentation annotations can be used to generate synthetic space-variant blur, we propose a Class-Centric Motion-Blur Augmentation (CCMBA) strategy. Our approach involves randomly selecting a subset of semantic classes present in the image and using the segmentation map annotations to blur only the corresponding regions. This enables the network to simultaneously learn semantic segmentation for clean images, images with egomotion blur, as well as images with dynamic scene blur. We demonstrate the effectiveness of our approach for both CNN and Vision Transformer-based semantic segmentation networks on PASCAL VOC and Cityscapes datasets. We also illustrate the improved generalizability of our method to complex real-world blur by evaluating on the commonly used deblurring datasets GoPro and REDS.