Nucleoside analogs are a major class of antiviral drugs. Some act by increasing the viral mutation rate causing “death by mutagenesis” of the virus. Their mutagenic capacity, however, may lead to an evolutionary safety concern. We define evolutionary safety as a probabilistic assurance that the treatment will not generate an increased number of epidemiologically concerning mutated virus progeny. We develop a mathematical framework to estimate the total mutant load produced with and without mutagenic treatment. We predict rates of appearance of virus mutants as a function of the timing of treatment and the immune competence of patients, employing various assumptions about the vulnerability of the viral genome and its potential to generate undesired phenotypes. We focus on the case study of Molnupiravir, which is an FDA-approved treatment against COVID-19. We estimate that Molnupiravir is narrowly evolutionarily safe, subject to the current estimate of parameters. Evolutionary safety can be improved by restricting treatment to individuals with a low clearance rate and by designing treatments that lead to a greater increase in mutation rate. We report a simple rule to determine the fold-increase in mutation rate required to obtain evolutionary safety which is also applicable to other pathogen-treatment combinations.