Human organ structure and function are important endophenotypes for clinical outcomes. Genome-wide association studies (GWAS) have identified numerous common variants associated with phenotypes derived from magnetic resonance imaging (MRI) of the brain and body. However, the role of rare protein-coding variations affecting organ size and function is largely unknown. Here we present an exome-wide association study that evaluates 596 multi-organ MRI traits across over 50,000 individuals from the UK Biobank. We identified 107 variant-level associations and 224 gene-based burden associations (67 unique gene-trait pairs) across all MRI modalities, including PTEN with total brain volume, TTN with regional peak circumferential strain in the heart left ventricle, and TNFRSF13B with spleen volume. The singleton burden model and AlphaMissense annotations contributed 8 unique gene-trait pairs including the association between an approved drug target gene of KCNA5 and brain functional activity. The identified rare coding signals elucidate some shared genetic regulation across organs, prioritize previously identified GWAS loci, and are enriched for drug targets. Overall, we demonstrate how rare variants enhance our understanding of genetic effects on human organ morphology and function and their connections to complex diseases.