Globally, in 2016, 1 out of 11 adults suffered from diabetes mellitus. Diabetic foot ulcers (DFU) are a major complication of this disease, which if not managed properly can lead to amputation. Current clinical approaches to DFU treatment rely on patient and clinician vigilance, which has significant limitations, such as the high cost involved in the diagnosis, treatment, and lengthy care of the DFU. We collected an extensive dataset of foot images, which contain DFU from different patients. In this DFU classification problem, we assessed the two classes as normal skin (healthy skin) and abnormal skin (DFU). In this paper, we have proposed the use of machine learning algorithms to extract the features for DFU and healthy skin patches to understand the differences in the computer vision perspective. This experiment is performed to evaluate the skin conditions of both classes that are at high risk of misclassification by computer vision algorithms. Furthermore, we used convolutional neural networks for the first time in this binary classification. We have proposed a novel convolutional neural network architecture, DFUNet, with better feature extraction to identify the feature differences between healthy skin and the DFU. Using 10-fold cross validation, DFUNet achieved an AUC score of 0.961. This outperformed both the traditional machine learning and deep learning classifiers we have tested. Here, we present the development of a novel and highly sensitive DFUNet for objectively detecting the presence of DFUs. This novel approach has the potential to deliver a paradigm shift in diabetic foot care among diabetic patients, which represent a cost-effective, remote, and convenient healthcare solution.