Information security culture has been studied as a systemic phenomenon that determines generation Z managers’ behavior in the digital environment. Internet addiction and digital anxiety are socio-psychological factors affecting individual digital hygiene habits and compliance with information security rules. The psychological portrait of generation Z managers has been revealed, how they differ from other generations, and what socio-psychological problems arise in this regard. Special attention has been paid to new social phenomena that have become widespread, such as the emergence of Internet addiction and digital anxiety among generation Z managers, and an explanation of these scientific terms and how they affect information security culture has been given. The structural components of information security culture (values and norms, knowledge and skills, daily practices, leadership, and organizational artifacts) and their relationship to management activities of generation Z people have been described. The analysis of what negative consequences in the context of management activities digital anxiety, Internet addiction, and digital hygiene non-observance can lead to at the level of an organization and personality as a whole has been carried out. For preventing and correcting Internet addiction and digital anxiety in generation Z managers in the context of digital hygiene and information security, a comprehensive approach to solving this scientific issue has been proposed, including both individual psychological strategies (digital detox, cognitive behavioral techniques, development of offline activities and social connections, manager’s digital hygiene, strengthening information security, and mindfulness practices), as well as organizational strategies (creating a culture of information security and digital well-being, reviewing performance metrics, and maintaining work-life balance).