The COVID-19 pandemic has drastically changed our lives. By increased screen time during the pandemic, social media (SM) could have significantly impacted adolescents’ and students’ mental health (MH). This literature review aims to synthesize the research on the impact of SM usage on MH of adolescents and students during the first year of the COVID-19 pandemic. A review of the published literature was conducted in April 2021, through a search of PubMed and Web of Science Core Collection databases. The search yielded 1136 records, with 13 articles selected for this review. Most of the included studies observed the negative impact of SM use on MH of adolescents and students, most noticeably observed were anxiety, depression and stress. More active and prolonged SM usage was associated with a negative impact on MH of adolescents and students. Two studies recorded some potentially positive effects, such as support in coping and providing a sense of connection for those who were isolated due to social distancing measures. Since this review focuses on the early period of the pandemic, future studies should investigate the long-term impact of SM use on adolescents and students MH, with all relevant elements that can enable adequate public health response.