We propose a mechanism for labor-market polarization based on the nonhomotheticity of demand that we call the income-driven channel. Our mechanism builds on a novel empirical fact: expenditure elasticities and production intensities in low- and high-skill occupations are positively correlated across sectors. Thus, as income grows, demand shifts towards expenditure-elastic sectors, and the relative demand for low- and high-skill occupations increases, causing labor-market polarization. A calibrated general-equilibrium model suggests this mechanism accounts for 90% and 35% of the increase in the wage-bill share of low- and high-skill occupations observed in the US during 1980-2016, and for 64% and 28% of the rise in the employment shares of low- and high-skill occupations. This mechanism is similarly important for the polarization of labor markets in Western Europe during 1980-2016, as well as in the US during earlier decades and, possibly, the near future.