Nuclear anxiety, which refers to the fear of nuclear war and its consequences, is expected to increase amid the Russian–Ukrainian War of 2022 (RUW-22). This study aimed to evaluate the prevalence of nuclear anxiety and its associated variables among university students in the Czech Republic during the first weeks of RUW-22. A cross-sectional survey-based study was carried out from March–April 2022, utilizing a digital self-administered questionnaire (SAQ) to collect data from the target population. The SAQ consisted of multiple-choice items inquiring about demographic characteristics; generalized anxiety symptoms using generalized anxiety disorder-7 (GAD-7); depressive symptoms using patient health questionnaire-9 (PHQ-9); and attitudes towards civilian uses of nuclear power, and nuclear war-related anxiety. Of the 591 participating students, 67.7% were females, 68.2% were Czech nationals, and 61.8% followed the RUW-22 news at least once daily. The mean GAD-7 score of our participants was 7.86 ± 5.32 (0–21); and their mean PHQ-9 score was 8.66 ± 6.29 (0–27). Regarding the civilian uses of nuclear power, most participants agreed that nuclear power was safe (64.5%), denied being afraid that civilian use of nuclear power might deteriorate their health (79.7%), and thought that public acceptance was important for building new nuclear power plants (56.9%). About 42.1% and 45.5% of the participants reported feeling depressed at the possibility of nuclear war and agreed that the chances that there would be a nuclear war in their lifetime were very high, respectively. When asked about their preparedness measures during the previous four weeks, less than one quarter (23.9%) reported looking for recommendations for protection against nuclear accidents, and less than one-fifth (19.3%) were looking for the nearest bomb shelter. The depression about nuclear war possibility was positively and relatively strongly correlated with the level of “feeling concerned about the RUW-22” (rs = 0.401), and it was moderately correlated with GAD-7 (rs = 0.377) and PHQ-9 (rs = 0.274) scores and weakly correlated with RUW-2-related news-following frequency (rs = 0.196). Within the limitations of the present study, nuclear anxiety was common among Czech university students. Its associated factors may include but are not limited to the female gender; common psychological disorders such as generalized anxiety and depression; RUW-22-related news following-frequency; and the level of “feeling concerned”.