This study examines the relationship between Facebook (FB) usage and addiction level, and sleep quality of university students. A Google Forms questionnaire was prepared and disseminated via the authors’ FB profile for university students to fill out. A total of 277, including two studying overseas, took part in this research. Among the survey respondents, over 60% (n = 144) were medical students (p = 0.000); over 30% (n = 84) were always logged into FB; the average and daily usage time of most was 5 to 60 min at a time (p = 0.009), and 3 to 5 h a day (p = 0.040), respectively. The respondents’ average sleep time was 7.11 h, but over 61% categorized their sleep quality as poor. It was also found that students from financial and management school were 4.23 times more at risk of FB addiction than the medical counterparts and were likely to be already addicted to FB as well as have a sleep disorder. Based on these results, it is suggested that university students, who fall in the high-risk category, be screened early to prevent them from developing social media addiction and sleep disorders. For improving youths’ health and sleep quality, future research should attach the importance to early screening for sleep disturbances caused by the internet and social media addiction.