Previous data support that mental health is affected during pandemic and lockdown situations. Yet, little is known about the positive factors that protect mental health during a lockdown. This study analyzed mental health status—particularly emotional problems—and the role of several sociodemographic and clinical variables; it also explored whether there is a positive relationship between self-compassion and better mental health status. A cross-sectional study was carried out in Spain with the participation of 917 fluent Spanish-speaking residents in a survey conducted approximately midway through the COVID-19 lockdown. The survey tested for anxiety, depression, and stress using the Depression Anxiety Stress Scale-21 (DASS-21), the Self-Compassion Scale (SCS) to measure self-compassion values, and the Perceived Vulnerability to Disease Questionnaire (PVDQ) to assess the degree of risk perceived by participants. Around 30% of the individuals surveyed (recruited by snowball sampling) showed clinically significant levels of anxiety, depression, and stress. The variables most frequently associated with anxiety, depression, and stress were low levels of self-compassion, age, gender, previous physical symptoms, a previous mental disorder, being a student, and perceived vulnerability to disease. We discuss the hypothetical protective role against anxiety, depression, and stress of certain skills such as self-compassion and the possibility that increasing self-compassion may be used to promote better mental health in similar situations.