Background The rollout of COVID-19 vaccines has brought vaccine hesitancy to the forefront in managing this pandemic. COVID-19 vaccine hesitancy is fundamentally different from that of other vaccines due to the new technologies being used, rapid development, and widespread global distribution. Attitudes on vaccines are largely driven by online information, particularly information on social media. The first step toward influencing attitudes about immunization is understanding the current patterns of communication that characterize the immunization debate on social media platforms. Objective We aimed to evaluate societal attitudes, communication trends, and barriers to COVID-19 vaccine uptake through social media content analysis to inform communication strategies promoting vaccine acceptance. Methods Social network analysis (SNA) and unsupervised machine learning were used to characterize COVID-19 vaccine content on Twitter globally. Tweets published in English and French were collected through the Twitter application programming interface between November 19 and 26, 2020, just following the announcement of initial COVID-19 vaccine trials. SNA was used to identify social media clusters expressing mistrustful opinions on COVID-19 vaccination. Based on the SNA results, an unsupervised machine learning approach to natural language processing using a sentence-level algorithm transfer function to detect semantic textual similarity was performed in order to identify the main themes of vaccine hesitancy. Results The tweets (n=636,516) identified that the main themes driving the vaccine hesitancy conversation were concerns of safety, efficacy, and freedom, and mistrust in institutions (either the government or multinational corporations). A main theme was the safety and efficacy of mRNA technology and side effects. The conversation around efficacy was that vaccines were unlikely to completely rid the population of COVID-19, polymerase chain reaction testing is flawed, and there is no indication of long-term T-cell immunity for COVID-19. Nearly one-third (45,628/146,191, 31.2%) of the conversations on COVID-19 vaccine hesitancy clusters expressed concerns for freedom or mistrust of institutions (either the government or multinational corporations) and nearly a quarter (34,756/146,191, 23.8%) expressed criticism toward the government’s handling of the pandemic. Conclusions Social media content analysis combined with social network analysis provides insights into the themes of the vaccination conversation on Twitter. The themes of safety, efficacy, and trust in institutions will need to be considered, as targeted outreach programs and intervention strategies are deployed on Twitter to improve the uptake of COVID-19 vaccination.