The rapid rise of non-communicable diseases (NCDs) becomes one of the serious health issues and the leading cause of death worldwide. In recent years, artificial intelligence-based systems have been developed to assist clinicians in decision-making to reduce morbidity and mortality. However, a common drawback of these modern studies is related to explanations of their output. In other words, understanding the inner logic behind the predictions is hidden to the end-user. Thus, clinicians struggle to interpret these models because of their black-box nature, and hence they are not acceptable in the medical practice. To address this problem, we have proposed a Deep Shapley Additive Explanations (DeepSHAP) based deep neural network framework equipped with a feature selection technique for NCDs prediction and explanation among the population in the United States. Our proposed framework comprises three components: First, representative features are done based on the elastic net-based embedded feature selection technique; second a deep neural network classifier is tuned with the hyper-parameters and used to train the model with the selected feature subset; third, two kinds of model explanation are provided by the DeepSHAP approach. Herein, (I) explaining the risk factors that affected the model’s prediction from the population-based perspective; (II) aiming to explain a single instance from the human-centered perspective. The experimental results indicated that the proposed model outperforms various state-of-the-art models. In addition, the proposed model can improve the medical understanding of NCDs diagnosis by providing general insights into the changes in disease risk at the global and local levels. Consequently, DeepSHAP based explainable deep learning framework contributes not only to the medical decision support systems but also can provide to real-world needs in other domains.