The Covid-19 disease has spread widely over the whole world since the beginning of 2020. Following the epidemic which started in Wuhan, China on January 30, 2020 the World Health Organization (WHO) declared a global health emergency and a pandemic. Researchers of different disciplines work along with public health officials to understand the SARS-CoV-2 pathogenesis and jointly with the policymakers urgently develop strategies to control the spread of this new disease. Recent findings have observed specific image patterns from computed tomography (CT) for patients infected by SARS-CoV-2 which are distinct from the other pulmonary diseases. In this paper, we propose an explainable-by-design that has an integrated image segmentation mechanism based on SLIC that improves the algorithm performance and the interpretability of the resulting model. In order to evaluate the proposed approach, we used the SARS-CoV-2 CT scan dataset that we published recently and has been widely used in the literature. The proposed Super-xDNN could obtain statistically better results than traditional deep learning approaches as DenseNet-201 and Resnet-152. Furthermore, it also improved the explainability and interpretability of its decision mechanism when compared with the xDNN basis approach that uses the whole image as prototype. The segmentation mechanism of Super-xDNN favored a decision structure that is more close to the human logic. Moreover, it also allowed the provision of new insights as a heat-map which highlights the areas with highest similarities with Covid-19 prototypes, and an estimation of the area affected by the disease.