Poverty remains a relevant problem in Brazil, potentially hindering the economic development of its regions. Applying the poverty convergence approach developed by Ravallion (2012), we analyze the complex interactions between poverty and economic growth in Brazilian municipalities. Using a dataset from 1991 to 2010, our results reveal a pattern of absolute income convergence across Brazilian municipalities, implying that regions with lower initial income levels tend to experience higher subsequent per capita income growth (the advantage of backwardness effect). In addition, we find that per capita income growth reduces the incidence of poverty (the advantage of the growth effect). Therefore, poverty should converge across Brazilian municipalities. However, the initial incidence of poverty hampered poverty convergence by reducing the impact of backwardness and the growth effect. Furthermore, spatial spillovers matter, as income growth in neighboring municipalities contributes to local poverty reduction; however, high poverty levels in surrounding areas weaken this beneficial effect. Our results underscore the importance of public policies in addressing and reducing poverty incidence as a strategy to promote economic growth in Brazilian regions.