Although secondhand smoke (SHS) exposure is predominant in Bangladesh, the adverse effect of SHS exposure on health-related behaviors, such as sleep quality, have remained an under-investigated area of the country’s public health landscape. Therefore, the purpose of this study was to examine the association between SHS exposure and poor sleep quality among non-smoking university students in Bangladesh. A cross-sectional survey was carried out between May and September 2022. SHS exposure (main predictor variable) and other covariates (e.g., age, sex, etc.) were measured using a self-reported questionnaire and sleep quality (outcome variable) was measured via the Pittsburgh Sleep Quality Index. Multiple logistic regression models investigated the association between SHS exposure and poor sleep quality. The study included 390 students (mean age: 22 years, 53.8% male). Approximately 41.8% of the participants reported SHS exposure, and 50.5% had poor sleep quality. Students exposed to SHS were more likely to have poor sleep quality compared to their counterparts (AOR = 1.61; 95% CI 1.01, 2.58). Subgroup analysis revealed poor sleep quality was 2-times higher among male students exposed to SHS than those male students without SHS exposure (AOR = 2.03; 95% CI 1.05, 3.93). No association was found in female students. Findings from this study warrant increased awareness and public health initiatives on the implications of SHS on health behaviors, such as sleep quality, in non-smoking Bangladeshi university students.