Genetic variants affecting pancreatic islet enhancers are central to T2D risk, but the gene targets of islet enhancer activity are largely unknown. We generate a high-resolution map of islet chromatin loops using Hi-C assays in three islet samples and use loops to annotate target genes of islet enhancers defined using ATAC-seq and published ChIP-seq data. We identify candidate target genes for thousands of islet enhancers, and find that enhancer looping is correlated with islet-specific gene expression. We fine-map T2D risk variants affecting islet enhancers, and find that candidate target genes of these variants defined using chromatin looping and eQTL mapping are enriched in protein transport and secretion pathways. At IGF2BP2, a fine-mapped T2D variant reduces islet enhancer activity and IGF2BP2 expression, and conditional inactivation of IGF2BP2 in mouse islets impairs glucose-stimulated insulin secretion. Our findings provide a resource for studying islet enhancer function and identifying genes involved in T2D risk.