Due to close contact with death, medical students may question their own and their patients’ dying process, especially with the impact of the COVID-19 pandemic on the increase in deaths. This situation provokes fear and negative attitudes towards dealing with patients and their environment. This study aimed to assess the level of fear of death and associated factors in medical students at a Peruvian university. A cross-sectional analytical study was conducted during March 2021 in human medicine students from the first to the seventh year. A validated survey including the Collet–Lester fear-of-death scale was applied. Factors associated with the fear-of-death score were evaluated by calculating linear regression coefficients (β). A total of 284 students were included. The median age was 22 years, and 58.1% were female. The mean Collet–Lester scale score was 2.79, and it was higher in the dimensions related to the death of others. Adjusted analysis showed that the score on this scale was lower in students aged 24–40 years compared to 17–21 years (β: −0.25; 95% CI: −0.46 to −0.04) and those who had no religious beliefs (β: −0.29; 95% CI: −0.53 to −0.04). In conclusion, fear of death was lower than reported in other investigations despite the COVID-19 situation, being much lower among older students and those without religious beliefs.