This paper examines the populational impact of the COVID-19 vaccinations for Brazil. Therefore, our analysis takes into account the time series of the daily number of deaths related to COVID-19 from March 17, 2020 until October 19, 2021 with 582 observations. Specifically, we apply the permutation entropy (H-s), statistical complexity (C-s) and Fisher information measure (F-s) to investigate the predictability of the daily deaths for COVID-19 considering two pandemic scenarios (until and after the extreme day). Based on these complexity measures, we construct the Complexity-Entropy causality plane (CECP) and Shannon Fisher causality plane (SFCP), which allows us to assess the disorder and estimate randomness inherent to the time series of the daily deaths for COVID-19 concerning these two pandemic scenarios. Our empirical results indicate that after the extreme day, the increase in the vaccinated population contingent led to a lower entropy, higher predictability, and lower death cases. Given this, we conclude that the COVID-19 vaccines in Brazil were a highly effective public health action. In the most extreme situation, Brazil had 4249 records of daily deaths on April 8, 2021, approximately 3.5 months after the first dose of the vaccine. After this extreme situation on April 9, 2021, the daily records of deaths decrease to a minimum of 130 deaths on October 19, 2021. Thus, there is a percentage variation of -96.44% in records of daily deaths. To the best of our knowledge, this work is the first to provide empirical evidence for the populational impact related to COVID-19 vaccines.