Background Problematic smartphone use (PSU) is an increasing public health concern among international students and may be linked to acculturative stress during cross-cultural adaptation. However, the psychological mechanisms underlying this association remain insufficiently understood. This study examined the association between acculturative stress and PSU among international students in Japan and tested the independent and sequential mediating roles of emotion regulation strategies and social anxiety. Methods A cross-sectional survey was conducted between March and September 2025 among 732 international students in Japan. Participants completed self-report measures of acculturative stress, cognitive reappraisal, expressive suppression, social anxiety, and PSU. A conceptual model comprising six hypotheses was tested using Pearson correlation analysis, confirmatory factor analysis, and structural equation modeling. Indirect effects were evaluated using 5,000 bootstrap resamples. Results The prevalence of PSU was 48.9%. Acculturative stress was positively associated with PSU (direct effect = 0.089, p < 0.001). Cognitive reappraisal (indirect effect = 0.043, p < 0.001), expressive suppression (indirect effect = 0.017, p < 0.001), and social anxiety (indirect effect = 0.033, p < 0.001) each significantly mediated this relationship. In addition, significant sequential indirect effects were observed through cognitive reappraisal followed by social anxiety, and through expressive suppression followed by social anxiety. The total indirect effect accounted for 58.3% of the total association between acculturative stress and PSU. Overall, the findings supported all six hypotheses proposed in the conceptual model. Conclusion The empirical testing and support of the proposed sequential mediation model represent an important contribution of this study and provide a novel framework for understanding the psychosocial correlates of PSU. The findings underscore the public health relevance of acculturative stress among international students and suggest that adaptive emotion regulation and social anxiety may be important targets for prevention. Universities and public health practitioners should consider culturally sensitive strategies to support international students' mental well-being and digital health behaviors.