Although internet addiction (IA) has been the subject of research in many countries, it is poorly studied in Bangladesh, and previous studies in the country have not examined potential mental health risk factors in relation to the development of IA. The present pilot study attempted to assess the prevalence and associated risk factors of IA among a convenience sample of recently graduated university students actively looking for a job (N = 284) from July to October 2018 in Rajshahi (a city in Bangladesh). The measures included socio-demographic and behavioral variables, the Internet Addiction Test (IAT), and the Depression, Anxiety, and Stress Scale. Surprisingly, no cases of IA were identified in the sample (i.e., the prevalence rate of IA was 0%) which may have been a consequence of the specific population sampled. A total of 3.9% of the participants (n = 11) were classified as excessive users (≥ 60 in IAT). Using regression analysis, the risk factors for excessive internet use were spending more time online (> 5 h daily) and experiencing psychiatric conditions (i.e., depression, stress). It is hoped the present pilot study will facilitate further study in Bangladesh with a more in-depth focus on the socio-demographic and psychiatric morbidities in excessive and problematic internet use. It is also speculated that job-seeking may be a situational protective risk factor for developing IA.