Background: Recently, the high prevalence of problematic digital media use among youth has become a public concern. Therefore, this study investigated digital citizenship's moderating effects on a supportive school environment, parental pressure to achieve, academic stress, problematic digital media use, and happiness in school-aged children. Methods: This cross-sectional study involved secondary data analysis of national data from the 11th Panel Study on Korean Children 2018 on 1342 families of fourth-grade students. Structural equation modeling assessed the relations among variables. Results: A multigroup analysis verified that digital citizenship significantly moderated the paths from supportive school environment to problematic digital media use, supportive school environment to happiness, and problematic digital media use to happiness. Specifically, problematic digital media use had a significant positive effect on happiness in the low-digital citizenship group and a significant negative effect in the high-digital-citizenship group. Conclusions: These findings indicate that digital citizenship as a competency should be fostered to prevent problematic digital media use.