Drug-Drug Interactions (DDIs) may hamper the functionalities of drugs, and in the worst scenario, they may lead to adverse drug reactions (ADRs). Predicting all DDIs is a challenging and critical problem. Most existing computational models integrate drug-centric information from different sources and leverage them as features in machine learning classifiers to predict DDIs. However, these models have a high chance of failure, especially for new drugs when all the information is not available. This paper proposes a novel Hypergraph Neural Network (HyGNN) model based on only the Simplified Molecular Input Line Entry System (SMILES) string of drugs, available for any drug, for the DDI prediction problem. To capture the drug chemical structure similarities, we create a hypergraph from drugs' chemical substructures extracted from the SMILES strings. Then, we develop HyGNN consisting of a novel attention-based hypergraph edge encoder to get the representation of drugs as hyperedges and a decoder to predict the interactions between drug pairs. Furthermore, we conduct extensive experiments to evaluate our model and compare it with several state-of-the-art methods. Experimental results demonstrate that our proposed HyGNN model effectively predicts DDIs and impressively outperforms the baselines with a maximum F1 score, ROC-AUC, and PR-AUC of 94.61%, 98.69%, and 98.68%, respectively. Finally, we show that our models also work well for new drugs.