Molecular interactions are significant resources for analyzing sophisticated biological systems. Identification of multifarious molecular interactions attracts increasing attention in biomedicine, bioinformatics, and human healthcare communities. Recently, a plethora of methods have been proposed to reveal molecular interactions in one specific domain. However, existing methods heavily rely on features or structures involving molecules, which limits the capacity of transferring the models to other tasks. Therefore, generalized models for the multifarious molecular interaction prediction (MIP) are in demand. In this paper, we propose a contrastive self-supervised graph neural network (CSGNN) to predict molecular interactions. CSGNN injects a mix-hop neighborhood aggregator into a graph neural network (GNN) to capture high-order dependency in the molecular interaction networks and leverages a contrastive self-supervised learning task as a regularizer within a multi-task learning paradigm to enhance the generalization ability. Experiments on seven molecular interaction networks show that CSGNN outperforms classic and state-of-the-art models. Comprehensive experiments indicate that the mix-hop aggregator and the self-supervised regularizer can effectively facilitate the link inference in multifarious molecular networks.