Social distancing was planned as a preventive measure to control the extensive spread of COVID-19. COVID-19-related deaths in Brazil were analyzed during the period of social distancing measures. Mortality data for COVID-19 was obtained from the Worldometer website (www.worldometer.info). Deaths were estimated up to the 31st day after the occurrence of the 5th COVID-19-related death in Brazil. Social distance was measured using Google's community mobility reports (https://www.google.com/covid19/mobility/). The Brazilian epidemic curves were interconnected, and mathematical models were evaluated to fit the mortality estimation curves. The optimistic model was defined in the opening period of social distancing and, therefore, in the lower mobility (40-60%). The realistic model was calculated according to relaxed social distance measures (<40%) and the pessimistic model was calculated based on the transmission rate between 2-3. Thus, the equations of the mathematical models provided the outcomes for the date of June 9, 2020, as follows: realistic model with 40,623 deaths, pessimistic model with 64,310 deaths and the optimistic model with a projection of 31,384 deaths. As a result of these analyzes, on May 24, 2020, there were a total of 22,965 deaths related to COVID-19, and those deaths included within the proposed mathematical models were 17,452 for the optimistic model, 22,623 for the realistic model and 32,825 for the pessimistic model. Thus, it is concluded that social distancing measures promoted by the Brazilian public managers contributes to the reduction in approximately ten thousand deaths related to COVID-19 in the current pandemic scenario.