We examine how gender-based occupational sorting before the release of ChatGPT relates to predicted exposure to generative AI and its potential implications for the gender wage gap. Using Swedish administrative data, we find that women are overrepresented in occupations predicted to be more affected by generative AI. Mechanical partial-equilibrium simulations, based on hypothesized deviations from the 2021 occupational and wage distribution and incorporating predicted AI exposure and task complementarity, show that generative AI can widen the gender wage gap through existing patterns of gender-based occupational sorting.