Social media is used for various purposes including entertainment, communication, information search, and voicing their thoughts and concerns about a service, product, or issue. The social media data can be used for information mining and getting insights from it. The World Health Organization has listed COVID-19 as a global epidemic since 2020. People from every aspect of life as well as the entire health system have been severely impacted by this pandemic. Even now, after almost three years of the pandemic declaration, the fear caused by the COVID-19 virus leading to higher depression, stress, and anxiety levels has not been fully overcome. This has also triggered numerous kinds of discussions covering various aspects of the pandemic on the social media platforms. Among these aspects is the part focused on vaccines developed by different countries, their features and the advantages and disadvantages associated with each vaccine. Social media users often share their thoughts about vaccinations and vaccines. This data can be used to determine the popularity levels of vaccines, which can provide the producers with some insight for future decision making about their product. In this article, we used Twitter data for the vaccine popularity detection. We gathered data by scraping tweets about various vaccines from different countries. After that, various machine learning and deep learning models, i.e., naive bayes, decision tree, support vector machines, k-nearest neighbor, and deep neural network are used for sentiment analysis to determine the popularity of each vaccine. The results of experiments show that the proposed deep neural network model outperforms the other models by achieving 97.87% accuracy.