Background Sudden infant death syndrome (SIDS) is the leading cause of post-neonatal infant death in high-income countries. Central respiratory system dysfunction seems to contribute to these deaths. Excitation that drives contraction of skeletal respiratory muscles is controlled by the sodium channel NaV1.4, which is encoded by the gene SCN4A. Variants in NaV1.4 that directly alter skeletal muscle excitability can cause myotonia, periodic paralysis, congenital myopathy, and myasthenic syndrome. SCN4A variants have also been found in infants with life-threatening apnoea and laryngospasm. We therefore hypothesised that rare, functionally disruptive SCN4A variants might be over-represented in infants who died from SIDS. Methods We did a case-control study, including two consecutive cohorts that included 278 SIDS cases of European ancestry and 729 ethnically matched controls without a history of cardiovascular, respiratory, or neurological disease. We compared the frequency of rare variants in SCN4A between groups (minor allele frequency <0·00005 in the Exome Aggregation Consortium). We assessed biophysical characterisation of the variant channels using a heterologous expression system. Findings Four (1·4%) of the 278 infants in the SIDS cohort had a rare functionally disruptive SCN4A variant compared with none (0%) of 729 ethnically matched controls (p=0·0057). Interpretation Rare SCN4A variants that directly alter NaV1.4 function occur in infants who had died from SIDS. These variants are predicted to significantly alter muscle membrane excitability and compromise respiratory and laryngeal function. These findings indicate that dysfunction of muscle sodium channels is a potentially modifiable risk factor in a subset of infant sudden deaths. Funding UK Medical Research Council, the Wellcome Trust, National Institute for Health Research, the British Heart Foundation, Biotronik, Cardiac Risk in the Young, Higher Education Funding Council for England, Dravet Syndrome UK, the Epilepsy Society, the Eunice Kennedy Shriver National Institute of Child Health & Human Development of the National Institutes of Health, and the Mayo Clinic Windland Smith Rice Comprehensive Sudden Cardiac Death Program.