Recent studies have documented the high prevalence of burnout among medicine and dentistry students, with potentially catastrophic consequences for both students and patients. Both environmental and personality factors play a part in burnout; perfectionism, a common trait in medicine students’ personalities, has been linked to psychological distress and increasing students’ vulnerability to burnout. Self-compassion, i.e., treating oneself kindly through hardship, has recently emerged as a buffer between perfectionism and psychological distress. While using a novel three-factor conceptualization of perfectionism (BIG3), this study aims to analyze if self-compassion has a protective role in the relationship between perfectionism and burnout, in a sample of medicine and dentistry students, through mediation analysis. We found that self-compassion significantly mediated the relationship between all three forms of perfectionism and burnout: as a partial mediator in self-critical and rigid perfectionism, as well as a full mediator in narcissistic perfectionism. Our findings underline self-compassion’s relevance in burnout prevention and management, supporting its use as an intervention target in burnout reduction programs and strategies.