(1) Background: Although the evidence is consistent that vaccines for COVID-19 effectively prevent severe illness or death, the rapid development of vaccines has led to increased beliefs about possible negative consequences and conspiracy theories about the vaccine. Several factors influence whether or not people decide to be vaccinated. Some studies suggest that our perception of what significant others do and think influences our behavior. (2) Methods: This study evaluates the predictive role of beliefs about negative consequences of the COVID-19 vaccine, conspiracy beliefs about this vaccine, and social influence on the intention to vaccinate against COVID-19 in three Latin American and Caribbean countries: Chile, Mexico, and Colombia. Using convenience sampling, 2075 adults from Chile (48.3%), Mexico (27.6%), and Colombia (24.6%) participated by answering an online questionnaire with variables of interest. (3) Results: Despite the differences between countries, the results showed that the proposed model is invariant and explains between 56-66% of the COVID19 vaccination intent. Specifically, controlling for age, socioeconomic status, political orientation, and educational level, we found that beliefs about the negative consequences of the COVID-19 vaccine were the main predictor followed by social influence. Beliefs in conspiracy theories did not predict vaccination intention (4) Conclusions: Considering these variables in campaigns to boost vaccination intention is discussed.