The COVID-19 pandemic will have impactful long-term effects on the global rise of poverty and social inequalities, potentially compromising the achievement of SDGs for poverty-related diseases. We aimed to evaluate the impact of poverty increases, and the mitigation effects of social protection policies, on HIV/AIDS and Tuberculosis (TB) in Brazil, one of the largest and most unequal LMICs. We integrated economic, mathematical, and epidemiological models to forecast the trends of HIV/AIDS and TB according to different future scenarios, showing that the implementation of social protection policies could mitigate long-lasting rises in poverty, avoiding -in the most pessimistic economic projections- an increase of 41% in the incidence and 50% in the mortality from HIV/AIDS, and of 32% in the incidence and 53% in the mortality from TB. Overall, more than 250 thousand cases and 43 thousand deaths from HIV/AIDS and TB could be averted up to 2030.