Background: The outbreak of the coronavirus disease (COVID-19) and its rapid spread may have led to individuals developing post-traumatic stress disorder (PTSD) and psychological distress. Under this context, teachers merit more attention as a group with high levels of work stress. The purpose of this study was to verify the relationship between PTSD and psychological distress and to explore sleep problems as a possible mediator in the relationship between PTSD and psychological distress, as well as the moderator of internet gaming disorders (IGD) in the relationship between sleep problems and psychological distress. Methods: A total of 11,014 Chinese primary and middle school teachers participated in this study. The survey was conducted online between 25 May and 30 June 2020. Results: PTSD was shown to have both a direct and indirect effect on teachers’ psychological distress. The indirect effect was mediated by sleep problems. IGD played a moderating role between sleep problems and psychological distress. Conclusions: During the COVID-19 pandemic, PTSD has been shown to have had a serious impact on the psychological stress of teachers, which was mediated by sleep problems. In addition, IGD raised the harm brought from sleep problems on teachers’ mental health.