A key step towards understanding psychiatric disorders that disproportionately impact female mental health is delineating the emergence of sex-specific patterns of brain organization at the critical transition from childhood to adolescence. Prior work suggests that individual differences in the spatial organization of functional brain networks across the cortex are associated with psychopathology and differ systematically by sex. We aimed to evaluate the impact of sex on the spatial organization of person-specific functional brain networks. We leveraged person-specific atlases of functional brain networks defined using nonnegative matrix factorization in a sample of n = 6437 youths from the Adolescent Brain Cognitive Development Study. Across independent discovery and replication samples, we used generalized additive models to uncover associations between sex and the spatial layout ("topography") of personalized functional networks (PFNs). Next, we trained support vector machines to classify participants' sex from multivariate patterns of PFN topography. Finally, we leveraged transcriptomic data from the Allen Human Brain Atlas to evaluate spatial correlations between sex differences in PFN topography and gene expression. Sex differences in PFN topography were greatest in association networks including the fronto-parietal, ventral attention, and default mode networks. Machine learning models trained on participants' PFNs were able to classify participant sex with high accuracy. Brain regions with the greatest sex differences in PFN topography were enriched in expression of X-linked genes as well as genes expressed in astrocytes and excitatory neurons. Sex differences in PFN topography are robust, replicate across large-scale samples of youth, and are associated with expression patterns of X-linked genes. These results suggest a potential contributor to the female-biased risk in depressive and anxiety disorders that emerge at the transition from childhood to adolescence.