Introduction Medical students have made particular use of smartphones during the COVID-19 pandemic. Although higher smartphone overuse has been observed, its effect on mental disorders is unclear. This study aimed to assess the association between smartphone overuse and mental disorders in Peruvian medical students during the COVID-19 pandemic. Methods A cross-sectional study was conducted in 370 students aged between 16 and 41 years (median age: 20) in three universities from July to October 2020. A survey including Smartphone Dependence and Addiction Scale, PHQ-9, and GAD-7 was applied. Prevalence ratios were estimated using generalized linear models. Results Smartphone overuse was a common feature among students (n = 291, 79%). Depressive symptoms were present in 290 (78%) students and anxiety symptoms in 255 (69%). Adjusted for confounders, addictive/dependent smartphone use was significantly associated with presence of depressive symptoms (PR = 1.29, 95% CI: 1.20-1.38 for dependent use; PR = 1.30, 95% CI: 1.12-1.50 for addictive use). Also, addictive/dependent smartphone use was significantly associated with presence of anxiety symptoms (PR = 1.59, 95% CI: 1.14-2.23 for dependent use; PR = 1.61, 95% CI: 1.07-2.41 for addictive use). Conclusions Our findings suggest that medical students exposed to smartphone overuse are vulnerable to mental disorders. Overuse may reflect an inappropriate way of finding emotional relief, which may significantly affect quality of life and academic performance. Findings would assist faculties to establish effective measures for prevention of smartphone overuse.