COVID-19 has brought speculations on potential transmission routes of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the causal agent of the pandemic. It is reported that the main route of virus transmission to be person-to-person by respiratory droplets; however, people have raised concerns on the possible transmission of SARS-CoV-2 to humans via food and packaging and its potential effects on food safety. This review discusses food safety issues in the COVID-19 pandemic and reveals its possible transmission in cold-chain food. The first outbreak of COVID-19 in late 2019 was associated with a seafood market in Wuhan, China, while the second outbreak of COVID-19 in June 2020 was also related to a seafood market in Beijing, China. As of 2020, several frozen seafood products linked with SARS-CoV-2 have been reported in China. According to the current survey and scientific studies, the risk of infection by SARS-CoV-2 from cold-chain food, food products, and food packaging is thought to be very low. However, studies on food cold chain contamination have shown that SARS-CoV-2 remained highly stable under refrigerated (4°C) and even in freezing conditions (−10 to −80°C). Since one mode of SARS-CoV-2 transmission appears to be touching contaminated surfaces, it is important to clean and sanitize food contact surfaces properly. Understanding food safety hazard risks is essential to avoid potential negative health effects and SARS-CoV-2 transmission in the food supply chain during the COVID-19 pandemic.