Genetic mutations can cause disease by disrupting normal gene function. Identifying the disease-causing mutations from millions of genetic variants within an individual patient is a challenging problem. Computational methods which can prioritize disease-causing mutations have, therefore, enormous applications. It is well-known that genes function through a complex regulatory network. However, existing variant effect prediction models only consider a variant in isolation. In contrast, we propose VEGN, which models variant effect prediction using a graph neural network (GNN) that operates on a heterogeneous graph with genes and variants. The graph is created by assigning variants to genes and connecting genes with an gene-gene interaction network. In this context, we explore an approach where a gene-gene graph is given and another where VEGN learns the gene-gene graph and therefore operates both on given and learnt edges. The graph neural network is trained to aggregate information between genes, and between genes and variants. Variants can exchange information via the genes they connect to. This approach improves the performance of existing state-of-the-art models.