The COVID-19 outbreak has affected the sports field unprecedentedly. The emergency alert has deprived athletes of training in a suitable environment, as they are faced with cancellations of relevant events in their sports careers. This situation can cause stress levels and other emotional disorders similar to those experienced by athletes during periods of injury. Since the relationship between psychological factors and sports injuries is well-studied, the Global Psychological Model of Sports Injury (MGPLD) is applied to this historical situation for athletes. The purpose of this study was to analyze the relationships between perfectionism and trait anxiety with indicators of mental health (mood, depression, state anxiety, and stress) in high-performance athletes during confinement due to the COVID-19 pandemic, as well as to explore the coping strategies that athletes have applied and whether they are perceived as useful for managing negative emotional states. A cross-sectional study was conducted through online questionnaires during April 2020, adapting the Psychological Assessment Protocol of the High-Performance Sports Center of Murcia (Spain), to assess the psychological effects of confinement in a cross-cultural sample of 310 athletes (141 women and 169 men) from different countries in Europe, Asia, and America, and from diverse sports disciplines. The protocol comprised six instruments that test perfectionism, trait anxiety, mood states, stress, depression, coping strategies, and sleep. It was answered online via Google Forms. The results show that maladaptive perfectionism was related to all the indicators of athletes' mental health. However, athletes' levels of anxiety, stress, and depressive symptoms are relatively low, and the use of coping strategies such as cognitive restructuring and emotional calm was associated with lower levels of negative emotional states. Besides, the Iceberg Profile, a suitable fit for the mental health model, is observed in the mood of athletes, both in men and in women, although women showed higher levels of anxiety, stress, and depression than men. A strong relationship was observed between maladaptive perfectionism and martial arts sports discipline, superior to other sports. In short, it can be concluded that high-performance athletes in the studied sample showed negative emotional state values below the expected average. Finally, the proposals for practical applications of the results collected are discussed.