Knee Osteoarthritis (OA) is one of the most common causes of physical disability worldwide associated with a significant personal and socioeconomic burden. Deep Learning approaches based on Convolutional Neural Networks (CNNs) achieved remarkable improvements in knee OA detection. Despite this success, the problem of early knee OA diagnosis from plain radiographs remains a challenging task. This is due to the high similarity between the X-ray images of OA and non-OA subjects and the disappearance of texture information regarding bone microarchitecture changes in the top layers during the learning process of the CNN models. To address these issues, we propose a Discriminative Shape-Texture Convolutional Neural Network (DST-CNN), which automatically diagnoses early knee OA from X-ray images. The proposed model incorporates a discriminative loss to improve class separability and deal with high inter-class similarities. In addition, a new Gram Matrix Descriptor (GMD) block is embedded in the CNN architecture to compute texture features from several intermediate layers and combine them with the shape features in the top layers. We show that merging texture features with deep ones leads to better prediction of the early stages of OA. Comprehensive experimental results on two large public databases, Osteoarthritis Initiative (OAI) and Multicenter Osteoarthritis Study (MOST) demonstrate the potential of the proposed network. Ablation studies and visualizations are provided for a detailed understanding of our proposed approach.