The coronavirus disease (COVID-19) outbreak has affected not only physical health but also mental health and psychological wellbeing. This narrative review aimed to map the literature on the psychological impact on the young generation of the COVID-19 pandemic, social restrictions, and extraordinary measures to curb the spread of coronavirus. We performed a systematic search of MEDLINE through PubMed and Web of Science [Science Citation Index Expanded, SCI-EXPANDED), Social Sciences Citation Index (SSCI), and Emerging Sources Citation Index (ESCI)] of all scientific literature published from May 2020 until 15 March 2021. Based on inclusion and exclusion criteria, a total of 15 articles were included. We conducted a narrative review. The reviewed articles suggested the impact of the pandemic and lockdown measures on young persons for several mental symptoms as well as anxiety, stress, depression, event-specific distress, decrease in psychological wellbeing, and changes in sleep habits. Psychological symptoms were related to the experience of several stressors, such as risk for reduction of academic perspectives, massive e-learning adoption, economic issues, social restrictions, and implications for daily life related to the COVID-19 outbreak. This narrative review points out the negative psychological impact of the pandemic outbreak and the high vulnerability of the young in the development of psychological distress, highlighting the relevant focus on the mental health of young people during the pandemic and the need for structured and tailored psychological support and interventions focused to the improvement of Quality of Life of university students after the pandemic experience.