As a platform of social media with high activity, Twitter has seen the discussion of many hot topics related to the COVID-19 pandemic. One such is the COVID-19 vaccination program, which has skeptics in several religious, ethnic, and socioeconomic groups, and Indonesia has one of the largest populations of various ethnicities and religions of countries worldwide. Diverse opinions based on skepticism about the effectiveness of vaccines can increase the number of people who refuse or delay vaccine acceptance. Therefore, it is important to analyze and monitor stances and public opinions on social media, especially on vaccine topics, as part of the long-term solution to the COVID-19 pandemic. This study presents the Indonesian COVID-19 vaccine-related tweets data set that contains stance and aspect-based sentiment information. The data were collected monthly from January to October 2021 using specific keywords. There are nine thousand tweets manually annotated by three independent analysts. We annotated each tweet with three labels of stance and seven predetermined aspects related to Indonesian COVID-19 vaccine-related tweets: services, implementation, apps, costs, participants, vaccine products, and general. The dataset is useful for many research purposes, including stance detection, aspect-based sentiment analysis, topic detection, and public opinion analysis on Twitter, especially on the policies regarding the prevention of pandemics.