Background: In super-ageing Japan, COVID-19 vaccinations were starting to reach older people as of June 2021, which raises the issue of vaccine literacy. This study focuses on family members who work and also care for their older parents, as they are at risk of COVID-19 and also risk transmitting COVID-19 to the parents they care for and potentially influencing their parents’ vaccine uptake. Such family carers are central to the approach in Japan to achieving a sustainable and resilient society in response to ageing. Contrasting family carers’ COVID-19 vaccine literacy with their overall health literacy provides insights into their preparedness for COVID-19 vaccinations. The purpose of this study is to understand how vaccine literacy, compared to health literacy, varies across family carers and the sources of information they use. Methods: Through a cross-sectional online survey, family carers’ vaccine literacy, health literacy and their sources of information, including mass media, social media, health and care professionals, family, colleagues, friends, and others, were assessed. The participants’ (n = 292) mean age was 53, with 44% women, and an average of 8.3 h per week caring for their parents. Results: Notwithstanding the increased risks from COVID-19 with age, COVID-19 vaccine literacy relative to health literacy for older family carers is lower on average, higher with increased provision of care, and more variable, resulting in a substantial proportion of older family carers with relatively low vaccine literacy. Conclusions: At this stage of vaccine rollout in Japan, family carers’ sources of information to inform COVID-19 vaccine literacy is distinct, including more national and local mass media versus less health and care professionals and informal networks, which indicates the importance of tailored health communication strategies to enhance vaccine literacy.