Discovering disease-disease association based on the underlying biological mechanisms is an essential biomedical task in modern biology as understanding these relationships will assist biologists in discovering the pathogenesis, diagnosis, and intervention of human diseases. Recently, deep learning on graph and graph neural networks have achieved promising performance in modeling complex biological structures and learning compact representations of interconnected data. Inspired by the success of graph neural networks in learning subgraph representations, we propose a novel framework, SNN-VGA, designed to predict potential disease comorbid pairs. We first model disease-associated genes as subgraphs in the protein-protein interactions network and learn disentangled disease module representations using a subgraph neural network model. The learned embeddings are leveraged by the variational graph auto-encoder to predict disease comorbidity in the disease-disease interactions network. Empirical results from a benchmark dataset demonstrate that our method performs competitively compared with the state-of-the-art model, with an AUROC of 0.96.