(1) Lockdown-related fatigue occurring during the COVID-19 pandemic is a complex problem that can be experienced in different social groups. The objective of the current study is to attempt to identify socio-demographic and lifestyle-related factors that determine the impact of fatigue on health in general as well as in physical, cognitive, and psychosocial terms and to determine whether, and to what extent, these were predictors of fatigue in nursing students during the COVID-19 pandemic. (2) The study was conducted by the diagnostic poll method between 20 March and 15 December 2021 among 894 nursing students at six Polish universities. To collect the data, a validated Modified Fatigue Impact Scale (MFIS) was used. (3) Students from the age group of ≤20 experienced a significantly greater impact of fatigue on health in general as well as in physical and cognitive terms. The study demonstrated a significant negative relationship between the year of study and the impact of fatigue on health in general terms (r = −0.12; p < 0.0001) and the analyzed health terms, on physical (r = −0.12; p < 0.0001), cognitive (r = −0.10; p < 0.002), and psychosocial (r = −0.07; p < 0.041). In predicting the impact of fatigue on health in general and physical terms, it was the variable related to a reduction in physical activity during the COVID-19 pandemic that had the greatest contribution, while for the cognitive and psychosocial functions, it was the number of meals consumed per day. (4) It is recognized that action is needed to reduce the impact of fatigue on student health by modifying the predictors related to student lifestyles.