Individual vulnerabilities, such as particular personality characteristics, may be important risk factors that can hinder the development of young musicians and affect their professional careers. This study aimed to examine the relationship between obsessive–compulsive personality disorder (OCPD) and rigid perfectionism, study addiction, and well-being among music students. It was hypothesized that OCPD is a strong risk factor for addictive studying; compulsive learning, however, is an addictive disorder with its own etiology, symptomatology, epidemiology, and course. A total of 255 students from various music academies in Poland participated in the study. It used the Bergen Study Addiction Scale, assessing seven core addiction symptoms related to studying; Five-Factor Obsessive Compulsive Inventory; Perceived Stress Scale; Hospital Anxiety and Depression Scale; Three-Item Loneliness Scale; and a single-item measure of learning engagement. Both study addiction and OCPD showed positive relationships with stress, anxiety, depression, and loneliness. Multiple hierarchical regression analyses showed that study addiction was related to well-being above and beyond OCPD and was more strongly associated with compromised functioning. Furthermore, mediation analyses indicated that study addiction is a full mediator between OCPD and stress, as well as loneliness, and a partial mediator for anxiety and depression. Moderation analyses revealed that OCPD was related to well-being only for those participants who scored low for study addiction. There was no significant relationship between OCPD and well-being for participants who scored high for study addiction. These results strongly indicate that OCPD is an important risk factor for study addiction although these are different disorders. Like students with high levels of OCPD, students with high levels of study addiction but low levels of OCPD experience reduced well-being. The polythetic cut-off score showed that 24.6% of young musicians could be addicted to studying. Due to the high prevalence of this disorder, further systematic studies among young musicians are highly warranted to prevent and provide better help with the problem.