Background: Smart phone use has become a part of people’s everyday life. However, when the lack of using the smart phone to establish and maintain electronic communication is related to psychological distress, such a behavior may be considered a modern-age phobia, or nomophobia (no mobile phone phobia). The aims of the present study were to investigate among a sample of young adults the associations between scores for nomophobia and symptoms of depression, anxiety, stress, insomnia, and obsessive–compulsive disorders. Methods: A total of 537 students (mean age: 25.52 years; 42.3% females) participated in the study. They completed a booklet of self-rating questionnaires covering sociodemographic information and symptoms of nomophobia, depression, anxiety, stress, insomnia, and obsessive–compulsive disorders. Results: Higher scores for nomophobia were associated with higher scores for depression, anxiety, and stress, but not with scores for insomnia and obsessive–compulsive disorders. The regression model confirmed that symptoms of anxiety predicted nomophobia. Conclusions: The present results support the assumption that nomophobia appears to be a mood disturbance related to stronger associations with symptoms of anxiety and, to a lesser extent, with symptoms of depression and stress. By contrast, nomophobia appeared to be unrelated to insomnia and symptoms of obsessive–compulsive disorders.