Once the first SARS-CoV-2 vaccine became available, mass vaccination was the main pillar of the public health response to the COVID-19 pandemic. It was very effective in reducing hospitalizations and deaths. Here, we discuss the possibility that mass vaccination might accelerate SARS-CoV-2 evolution in antibody-binding regions compared to natural infection at the population level. Using the evidence of strong genetic variation in antibody-binding regions and taking advantage of the similarity between the envelope proteins of SARS-CoV-2 and influenza, we assume that immune selection pressure acting on these regions of the two viruses is similar. We discuss the consequences of this assumption for SARS-CoV-2 evolution in light of mathematical models developed previously for influenza. We further outline the implications of this phenomenon, if our assumptions are confirmed, for the future design of SARS-CoV-2 vaccination strategies.