Carpal tunnel syndrome (CTS) is a common and disabling condition of the hand caused by entrapment of the median nerve at the level of the wrist. It is the commonest entrapment neuropathy, with estimates of prevalence ranging between 5-10%. Here, we undertake a genome-wide association study (GWAS) of an entrapment neuropathy, using 12,312 CTS cases and 389,344 controls identified in UK Biobank. We discover 16 susceptibility loci for CTS with p < 5 × 10-8. We identify likely causal genes in the pathogenesis of CTS, including ADAMTS17, ADAMTS10 and EFEMP1, and using RNA sequencing demonstrate expression of these genes in surgically resected tenosynovium from CTS patients. We perform Mendelian randomisation and demonstrate a causal relationship between short stature and higher risk of CTS. We suggest that variants within genes implicated in growth and extracellular matrix architecture contribute to the genetic predisposition to CTS by altering the environment through which the median nerve transits.