In cancer, recurrent somatic single-nucleotide variants—which are rare in most paediatric cancers—are confined largely to protein-coding genes1–3. Here we report highly recurrent hotspot mutations (r.3A>G) of U1 spliceosomal small nuclear RNAs (snRNAs) in about 50% of Sonic hedgehog (SHH) medulloblastomas. These mutations were not present across other subgroups of medulloblastoma, and we identified these hotspot mutations in U1 snRNA in only <0.1% of 2,442 cancers, across 36 other tumour types. The mutations occur in 97% of adults (subtype SHHδ) and 25% of adolescents (subtype SHHα) with SHH medulloblastoma, but are largely absent from SHH medulloblastoma in infants. The U1 snRNA mutations occur in the 5′ splice-site binding region, and snRNA-mutant tumours have significantly disrupted RNA splicing and an excess of 5′ cryptic splicing events. Alternative splicing mediated by mutant U1 snRNA inactivates tumour-suppressor genes (PTCH1) and activates oncogenes (GLI2 and CCND2), and represents a target for therapy. These U1 snRNA mutations provide an example of highly recurrent and tissue-specific mutations of a non-protein-coding gene in cancer.