With the onset of COVID-19 pandemic, social media has rapidly become a crucial communication tool for information generation, dissemination, and consumption. In this scoping review, we selected and examined peer-reviewed empirical studies relating to COVID-19 and social media during the first outbreak starting in November 2019 until May 2020. From an analysis of 81 studies, we identified five overarching public health themes concerning the role of online social platforms and COVID-19. These themes focused on: (i) surveying public attitudes, (ii) identifying infodemics, (iii) assessing mental health, (iv) detecting or predicting COVID-19 cases, (v) analyzing government responses to the pandemic, and (vi) evaluating quality of health information in prevention education videos. Furthermore, our review highlights the paucity of studies on the application of machine learning on social media data related to COVID-19 and a lack of studies documenting real-time surveillance developed with social media data on COVID-19. For COVID-19, social media can play a crucial role in disseminating health information as well as tackling infodemics and misinformation.