Background Academic stress is a significant factor affecting students’ psychological well-being, particularly in higher education. Understanding the mediating roles of social support and self-efficacy can provide insights into how these factors influence students’ psychological well-being in public and private universities. Methods The study examined the mediating roles of social support and self-efficacy in the relationship between academic stress and psychological well-being among university students in Mogadishu, Somalia. Utilizing a stratified sampling technique, data were collected from 663 students across public (52.6%) and private (47.4%) universities through a structured questionnaire and analyzed using path analysis to assess direct and indirect effects. Structural equation modeling technique was used for data analysis. Results The analysis revealed a significant direct effect of academic stress on psychological well-being (β = 0.133, p = 0.000). Academic stress was not significantly related to social support (β = 0.128, p = 0.066) and self-efficacy (β = 0.075, p = 0.099). However, both social support (β = 0.059, p = 0.000) and self-efficacy (β = 0.838, p = 0.000) were significantly related to psychological well-being. The mediating analysis showed that social support partially mediated the relationship between academic stress and psychological well-being (Indirect effect = 0.070, CI [-0.036, 0.197], p = 0.000), while self-efficacy did not mediate this relationship (Indirect effect = 0.063, CI [0.054, 0.218], p = 0.097). Conclusions The findings suggest a significant positive impact of academic stress on psychological well-being, while social support partially mediates this relationship, highlighting its buffering role. Conversely, self-efficacy, although positively contributing to psychological well-being, does not mediate the effect of academic stress. These results underscore the importance of robust social support systems and targeted interventions to enhance students’ coping mechanisms and overall psychological well-being. Study limitations and implication are discussed.