Systematic study of tissue-specific function of enhancers and their disease associations is a major challenge. We present an integrative machine-learning framework, FENRIR, that integrates thousands of disparate epigenetic and functional genomics datasets to infer tissue-specific functional relationships between enhancers for 140 diverse human tissues and cell types, providing a regulatory-region-centric approach to systematically identify disease-associated enhancers. We demonstrated its power to accurately prioritize enhancers associated with 25 complex diseases. In a case study on autism, FENRIR-prioritized enhancers showed a significant proband-specific de novo mutation enrichment in a large, sibling-controlled cohort, indicating pathogenic signal. We experimentally validated transcriptional regulatory activities of eight enhancers, including enhancers not previously reported with autism, and demonstrated their differential regulatory potential between proband and sibling alleles. Thus, FENRIR is an accurate and effective framework for the study of tissue-specific enhancers and their role in disease. FENRIR can be accessed at fenrir.flatironinstitute.org/.