Background Social media use has been linked to poor sleep outcomes among university students in the cyber age, but the association between the negative consequences of social media use and sleep problems is not yet well understood. The present study investigated the relationships among social media usage, social media fatigue (SMF), fear of missing out (FoMO), social media addiction (SMA) and sleep quality in university students. Method An online survey was administered to 2744 respondents that included the Pittsburgh Sleep Quality Index (PSQI); questionnaires evaluating FoMO, SMF, and SMA; and questions regarding sleep duration, social media use, health status, and demographic information. Result A total of 19.9% of respondents suffered from sleep disturbance. A total of 15.6% of participants had sleep durations less than 5 h, and 21.6% of subjects had sleep durations longer than 9 h. Sleep quality was positively associated with SMF (OR = 1.387, 95% CI: 1.103 similar to 1.743), and SMA (OR = 1.415, 95% CI: 1.118 similar to 1.791). The relationship between FoMO and sleep disturbance was not significant. Compared to a sleep duration > 9 h, SMF increased the risk of shorter sleep durations [5-6 h sleep (OR = 2.226, 95% CI: 1.132 similar to 4.375), 6-7 h sleep (OR = 1.458, 95% CI: 1.061 similar to 2.002), and 7-8 h sleep (OR = 1.296, 95% CI: 1.007 similar to 1.670)]. FoMO and SMA did not significantly affect sleep duration. In addition, SMA (OR = 3.775, 95% CI: 3.141 similar to 4.537), FoMO (OR = 3.301, 95% CI: 2.753 similar to 3.958), and sleep disorders (OR = 1.284, 95% CI: 1.006 similar to 1.638) increased SMF. Conclusion Upon experiencing negative consequences of social media use, such as SMF and SMA, university students were likely to experience sleep problems. Further research exploring the interventions that improve sleep and alleviate negative consequences of social media use should be conducted.