The 2019 novel coronavirus disease (COVID-19) is a global threat that has negative impacts on individuals’ physical and mental health. Here, we explore if disordered social media use promotes fear of COVID-19, which in turn increases stress and depression in users. The study also explores several risk and protective factors that may affect the relationship between fear of COVID-19 and stress and depression. There were 174 participants that completed an online survey that measured disordered social media use, fear of COVID-19, perceived stress, and depression symptomatology. We found that disordered social media use predicts perceived stress indirectly through fear of COVID-19. Disordered social media use had a direct relationship with depression scores and this relationship is mediated by fear of COVID-19. We also found that the positive relationship between fear of COVID-19 and perceived stress is stronger for older people than younger people. The psychological impact of COVID-19 may be exacerbated by content promoting the fear of COVID-19 that users will be exposed to on social media.