Background: With the increase in communication technologies, the internet has become an indispensable tool in the life of the individual. Several studies report on the advantages of this resource; however, there is still a group of individuals who use the internet excessively. The aim of this study was to explore the relationships between internet addiction, daytime sleepiness, and family communication in adolescents. Methods: A total of 340 adolescents aged between 12 and 17 years participated in this study. All completed the sociodemographic questionnaire, the internet addiction test, the pediatric daytime sleepiness scale, and the family communication scale. Results: The results indicate that 64.1% of the adolescents had mild to moderate addiction to the internet. The main results suggest that internet addiction in adolescents is negatively associated with family communication and positively associated with excessive daytime sleepiness. It was also observed that gender had a significant effect on daytime sleepiness, with female participants having more excessive daytime sleepiness. Regarding age, the results indicate higher values of internet addiction among younger adolescents. Conclusions: In view of the above, it is considered important to develop preventive actions with a view to healthy family communication, with the adoption of sleep hygiene habits and the promotion of healthy use of the internet.