Cryopreservation of human gametes and embryos as well as human reproductive tissues has been characterized as an essential process and aspect of assisted reproductive technology (ART). Notably, sperm cryopreservation is a fundamental aspect of cryopreservation in oncological patients or patients undergoing gonadotoxic treatment. Given that there is a risk of contamination or cross-contamination, either theoretical or real, during the procedures of cryopreservation and cryostorage, both the European Society for Human Reproduction and Embryology (ESHRE) and the American Society for Reproductive Medicine (ASRM) have provided updated guidelines for preventing or reducing the contamination risk of sexually transmitted viruses. Given the ongoing and worldwide COVID-19 pandemic, there is considerable interest in what measures should be taken to mitigate SARS-CoV-2 contamination during cryopreservation and cryostorage of semen samples. The SARS-CoV-2 virus is the virus that causes COVID-19, and whose transmission and infection is mainly aerosol-mediated. Several ART professional societies, including ESHRE and ASRM have proposed measures to mitigate the spread of the SARS-CoV-2 virus. Whether the proposed safety directives are enough to mitigate the possible SARS-CoV-2-contamination of sperm samples during cryopreservation or whether the policies should be re-evaluated will be discussed in this review. Additionally, insights regarding the possible impact of COVID-19 vaccination on the safety of sperm cryopreservation will be discussed.