Using 1979-2019 Current Population Survey data, we study the effect of state and federal minimum wage policies on gender, race, and ethnic inequality. We find that minimum wages substantially reduce intergroup wage inequality at least up to the 20th wage percentile, with no evidence of adverse employment effects. We conduct counterfactual simulations of between-group inequality due to minimum wage changes since 1979. Declines in the real minimum wage in the 1980s slowed progress in narrowing between-group inequality. Relatively small changes in minimum wages during 1989-1998 and 1998-2007 meant little role for the minimum wage over those time spans. Since 2007, several states have steeply raised their minimum wages, especially raising Hispanics’ relative wages, because they earn low wages and reside disproportionately in those states. Finally, we find that raising the federal minimum wage to $12/hour in 2020 dollars ($14.49 in 2025Q2 dollars) would reduce existing between-group wage gaps below the 15th percentile by 25-50%.