Introduction: The extensive availability of the internet has led to the recognition of problematic internet use (so-called internet addiction—IA) mostly concerning adolescents. Aim: Here, we present a study focusing on the prevalence and risk factors of internet addiction in Hungarian high school students, using a questionnaire-based survey. Results: Overall, 3000 paper-based questionnaires were successfully delivered and 2540 responses were received (response rate of 84.6%). A total of 1309 males (mean age 17.6 ± 1.43 years) (51.5%) and 1231 females (mean age 17.5 ± 1.4 years) (48.5%) took part in our study. Internet addiction was detected in 486 (19.1%) students (232 males, mean age 17.6 ± 1.35 years, and 254 females, mean age 17.34 ± 1.37 years) based on the Problematic Internet Use Questionnaire. In a multivariate analysis, age (age of 17, OR = 3.688, p < 0.001), family status (living without parents) (OR = 2.091, p = 0.034), the size of the household (more than five people per household) (OR = 2.546, p = 0.026), spending more than 6 h online (OR = 5.457, p < 0.001), and daily time interval (OR = 84.316, p < 0.001) were significantly associated with internet addiction. Alcohol use (OR = 10.341, p = 0.001), drug intake (OR = 6.689, p = 0.001) and musculoskeletal disorders (OR = 3.966, p = 0.047) were also strongly associated with IA. Conclusion: A significant proportion of our students suffered from IA, which is associated with substance intake (possible abuse) and musculoskeletal pain in the multivariate analysis. Our study also draws attention to the preventable risk factors of IA, such as working hours or nighttime internet use, number of hours spent online and family surroundings.