This study aims to establish a link between disturbances in the night sleep habitus, quality of sleep, and daytime sleepiness in adolescents with Internet addiction and different types of content consumed. Methods: This is a cross-sectional observational study of a school sample in three large cities in Central Siberia. 4,615 schoolchildren of 12–18 years old were examined. The Russian-language versions of the Chen Internet Addiction Scale, the Game Addiction Scale for Adolescents, and the Social Media Disorder Scale were used to identify Internet addiction. Questions from the Pittsburgh Sleep Quality Index questionnaire were used to assess nighttime sleep. Daytime sleepiness was assessed using the Pediatric Daytime Sleepiness Scale questionnaire. Results: Adolescents with Internet addiction go to bed and wake up late; they are characterized by a decrease in the duration of nighttime sleep, an increase in sleep onset latency, and frequent nighttime awakenings, as well as more pronounced daytime sleepiness. Among the sleep parameters studied, the indicators of daytime sleepiness and night awakening scales have the highest effect size in Internet-addicted adolescents, regardless of the media consumed. Conclusion: Internet-addicted adolescents are characterized by significant disturbances in the quality of nighttime sleep and excessive daytime sleepiness, which requires appropriate psychological correction.