The implementation of mandatory stay-at-home and isolation policies during the COVID-19 pandemic has resulted in people relying more on smartphone use to obtain the latest developments regarding the pandemic, interact with people, and for entertainment. Unfortunately, as people spend more time participating in Internet activities, they are more likely to encounter problematic internet use (PIU) issues. The main purpose of this study was to examine the association between two kinds of PIU [problematic smartphone use (PSU) and problematic social media use (PSMU)], psychological distress, and sleep problems. In addition, the moderating effect of sleep problems was examined. A total of 11014 school teachers completed the online survey. The participants were divided into two (high and low sleep problem) groups, according to the severity of their sleep problems, for comparison. The research conducted a comparison between the degree of PIU and psychological distress, and then provided correction for the two groups separately. The results indicated that the high sleep problem group exhibited significantly greater psychological distress [mean () = 12.94 (11.29)] than the low sleep problem group [(mean () = 3.42 (6.57)]. Both PSU and PSMU were positively correlated with psychological distress in the two groups. The moderating effect of sleep problems was supported and PSMU was more harmful to psychological distress in the high sleep problem group, while the effect of PSU on psychological distress was not significantly different between the two groups.