The aim of this study was to examine the relationship of social media addiction with sleep quality and psychological problems in high school students. The study is a cross-sectional, correlational type. The study was conducted with 1,274 students receiving education in a district located in the western region of Turkey. For the collection of the data, a Descriptive Information Form, the Social Media Addiction Scale for Adolescents (SMASA), the Strengths and Difficulties Questionnaire (SDQ), the Sleep Quality Scale (SQS) and the Sleep Variables Questionnaire (SVQ) were used. Among the high school students who participated in the research, 49.3% stated that they had been using social media for 1–3 years, 53.9% reported that they spent 1–3 h per day on social media, and 42.8% stated that they placed their telephone under their pillow or beside their bed while sleeping. Students’ mean scores were 16.59 ± 6.79 (range: 9–45) for the SMASA, 16.54 ± 4.27 (range: 0–40) for total difficulties, and 14.18 ± 1.56 (range: 7–21) for the SQS, while their sleep efficiency value was 97.9%. According to the research model, difficulties experienced by high school students increase their social media addiction, while they decrease prosocial behaviours. Social media addiction in high school students decreases students’ sleep efficiency (p < 0.05). It is considered important to conduct further public health studies for children and adolescents related to the risks caused by the excessive use of technology, the consequences of social media addiction, measures to protect psychological health, sleep programmes and the importance of sleep quality.