COVID-19 is a widely spread disease, and in order to overcome its spread, vaccination is necessary. Different vaccines are available in the market and people have different sentiments about different vaccines. This study aims to identify variations and explore temporal trends in the sentiments of tweets related to different COVID-19 vaccines (Covaxin, Moderna, Pfizer, and Sinopharm). We used the Valence Aware Dictionary and Sentiment Reasoner (VADER) tool to analyze the public sentiments related to each vaccine separately and identify whether the sentiments are positive (compound ≥ 0.05), negative (compound ≤ −0.05), or neutral (−0.05 < compound < 0.05). Then, we analyzed tweets related to each vaccine further to find the time trends and geographical distribution of sentiments in different regions. According to our data, overall sentiments about each vaccine are neutral. Covaxin is associated with 28% positive sentiments and Moderna with 37% positive sentiments. In the temporal analysis, we found that tweets related to each vaccine increased in different time frames. Pfizer- and Sinopharm-related tweets increased in August 2021, whereas tweets related to Covaxin increased in July 2021. Geographically, the highest sentiment score (0.9682) is for Covaxin from India, while Moderna has the highest sentiment score (0.9638) from the USA. Overall, this study shows that public sentiments about COVID-19 vaccines have changed over time and geographically. The sentiment analysis can give insights into time trends that can help policymakers to develop their policies according to the requirements and enhance vaccination programs.