Schizophrenia is a highly heritable disorder for which anatomical brain alterations have been repeatedly reported in clinical samples. Unaffected at-risk groups have also been studied in an attempt to identify brain changes that do not reflect reverse causation or treatment effects. However, no robust associations have been observed between neuroanatomical phenotypes and known genetic risk factors for schizophrenia. We tested subcortical brain volume differences between 49 unaffected participants carrying at least one of the 12 copy number variants associated with schizophrenia in UK Biobank and 9063 individuals who did not carry any of the 93 copy number variants reported to be pathogenic. Our results show that CNV carriers have reduced volume in some of the subcortical structures previously shown to be reduced in schizophrenia. Moreover, these associations partially accounted for the association between pathogenic copy number variants and cognitive impairment, which is one of the features of schizophrenia.