Genetic studies promise to provide insight into the molecular mechanisms underlying type 2 diabetes (T2D). Variants associated with T2D are often located in tissue-specific enhancer clusters or super-enhancers. So far, such domains have been defined through clustering of enhancers in linear genome maps rather than in three-dimensional (3D) space. Furthermore, their target genes are often unknown. We have created promoter capture Hi-C maps in human pancreatic islets. This linked diabetes-associated enhancers to their target genes, often located hundreds of kilobases away. It also revealed >1,300 groups of islet enhancers, super-enhancers and active promoters that form 3D hubs, some of which show coordinated glucose-dependent activity. We demonstrate that genetic variation in hubs impacts insulin secretion heritability, and show that hub annotations can be used for polygenic scores that predict T2D risk driven by islet regulatory variants. Human islet 3D chromatin architecture, therefore, provides a framework for interpretation of T2D genome-wide association study (GWAS) signals.