Decades ago development scholars argued that the productive structure of a country (i. e. the mix of industries operating in the country) constrains its ability to generate and distribute income. They were correct! It was recently shown that the mix of products that a country exports is predictive of its future pattern of diversification and economic growth. But what is the link between a country's productive structure and its ability to distribute income? Here, we combine methods from econometrics, network science, and economic complexity, together with data on income inequality and world trade, to show that countries exporting complex products have lower levels of income inequality than countries exporting simpler products. Using multivariate regression analysis, we show that economic complexity is a significant and negative predictor of income inequality and that this relationship is robust to controlling for aggregate measures of income, institutions, export concentration, and human capital. Moreover, we introduce a measure that associates a product to a level of income inequality equal to the average GINI of the countries exporting that product (weighted by the share the product represents in that country’s export basket). The Product-GINI index, or PGI, can provide important insights on the constraints to inequality imposed by a country's productive structure. Finally, we integrate our results to the Observatory of Economic Complexity, an online resource that allows its users to visualize the structural transformation of over 150 countries and their associated changes in income inequality during 1963–2008.