The combinatorial effect of genetic variants is often assumed to be additive. Although genetic variation can clearly interact non-additively, methods to uncover epistatic relationships remain in their infancy. We develop low-signal signed iterative random forests to elucidate the complex genetic architecture of cardiac hypertrophy. We derive deep learning-based estimates of left ventricular mass from the cardiac MRI scans of 29,661 individuals enrolled in the UK Biobank. We report epistatic genetic variation including variants close to CCDC141 , IGF1R , TTN , and TNKS. Several loci where variants were deemed insignificant in univariate genome-wide association analyses are identified. Functional genomic and integrative enrichment analyses reveal a complex gene regulatory network in which genes mapped from these loci share biological processes and myogenic regulatory factors. Through a network analysis of transcriptomic data from 313 explanted human hearts, we found strong gene co-expression correlations between these statistical epistasis contributors in healthy hearts and a significant connectivity decrease in failing hearts. We assess causality of epistatic effects via RNA silencing of gene-gene interactions in human induced pluripotent stem cell-derived cardiomyocytes. Finally, single-cell morphology analysis using a novel high-throughput microfluidic system shows that cardiomyocyte hypertrophy is non-additively modifiable by specific pairwise interactions between CCDC141 and both TTN and IGF1R . Our results expand the scope of genetic regulation of cardiac structure to epistasis.