Background: The COVID-19 pandemic has changed the way we conduct daily life, as well as sports training and sports competitions. Given the stress produced by COVID-19, and the “bubble” safety measures for the World Sambo Championship, held in Novi Sad, from the 6th to the 8th of November, 2020, athletes might have experienced more stress than athletes normally would in non-pandemic conditions. Therefore, the current study aimed to create a psychological profile of sambo athletes participating in the Sambo World Championship and living in this condition. Methods: One-hundred-fifteen participants took part in the study, completing the Profile of Mood Scale (POMS), the Pittsburg Sleep Quality Index, the Perceived Stress Scale (PSS), and the Fear of COVID-19 Scale. A mediation model with Fear of COVID-19 predicting both stress level directly and stress level through mood disturbance was hypothesized. Gender differences were evaluated through t-test. Results: The results showed that the sample presented higher levels of stress but no problems in sleeping. In particular, data analysis confirmed an indirect effect of Fear of COVID on Perceived stress through mood disturbance (β = 0.14, Z = 2.80, and p = 0.005), but did not have a significant impact on the direct effect (β = −0.04, Z = −0.48, and p = 0.63). Gender differences emerged in the perceived stress level (t = −2.86, df = 114, and p = 0.005) and daytime dysfunction (t = −2.52, df = 114, and p = 0.01) where females scored higher than males for both aspects. Conclusion: The athletes participating to the World Sambo Championship experienced stress levels determined by the mood disturbance produced by the fear of the COVID-19 pandemic. Female athletes were more stressed and showed higher daytime dysfunction. The findings of the current study are useful to understand the psychological profile of the athletes competing in the “bubble” conditions during COVID-19 pandemic.