The development of COVID-19 vaccines has been crucial in fighting the pandemic. Misinformation about COVID-19 vaccines on social media is a major challenge, as this is thought to contribute to vaccine hesitancy. Here, we review the research on misinformation about COVID-19 vaccines spread on social media platforms. The review is registered with the PROSPERO international register of systematic reviews (CRD42021277524). We performed a literature search on 9 September 2021 and searched PubMed, PsycINFO, ERIC, Embase, Cochrane Library, and the Cochrane COVID-19 Study Register. We included publications in peer-reviewed journals that fulfilled all following criteria- Original empirical studies, studies that assessed social media and misinformation, studies that dealt with vaccine hesitancy, and studies about the COVID-19 vaccine. Publications were excluded if data were gathered before Phase III in the first COVID-19 vaccine development (from July 27 2020 to November 13, 2020). The narrative qualitative synthesis was undertaken with the guidance of the PRISMA 2020 Statement and the Synthesis Without Meta-analysis reporting guideline. The risk of bias was assessed according to The Joanna Briggs Institute (JBI) Critical Appraisal tool. Ratings of the certainty of evidence were based on recommendations from the GRADE Working Group. The search amounted to 757 records, with 45 articles selected for the review. There are many types of misinformation that are spread on social media platforms. We identified three main areas of misinformation- Medical misinformation, vaccine development, and conspiracies. To prevent these misconceptions from taking hold, health authorities should openly address and discuss these false claims with both cultural and religious awareness in mind. Our review showed that there is a need to examine the effect of social media misinformation on vaccine hesitancy with a more robust experimental design. Furthermore, our review also demonstrated that more studies are needed from the Global South and on other social media platforms than the major platforms such as Twitter.