Migrant workers are at a greater risk of having low mental well-being compared to their local counterparts. The Japanese government accepts migrants through its Technical Intern Training programs, but the factors associated with their mental well-being remain unclear. This study aimed to (1) assess trainees’ competence and importance in daily activities and (2) examine the association between their competence and mental well-being. We conducted a cross-sectional study using self-administered questionnaires. We recruited trainees through their supervising organizations and social media. We used the Occupational Self-Assessment tool to measure competence and importance in daily activities and the World Health Organization-5 Well-being Index to measure mental well-being. Hierarchical regression analysis was used to examine the association between competence and mental well-being. Among 383 trainees, 30.6% felt difficulty expressing themselves, and 27.4% felt difficulty accomplishing goals. Almost 50% valued self-care, working towards their goals, and managing their finances. Higher competence scores were associated with higher mental well-being scores (B = 0.76; 95% CI = 0.52, 1.00). Competence may be a key to having higher mental well-being among migrant trainees in Japan. A supportive and enabling environment, as well as mental health promotion at the community level, may improve trainees’ competence in daily activities.