Few studies have examined the intentions of parents and guardians to vaccinate their children younger than 18 years against COVID-19 in Ghana. Parents are the decision makers for children younger than 18 years; therefore, we examined parents’ and guardians’ intentions to accept the COVID-19 vaccines for their children. An online survey was conducted among 415 parents and guardians in Ghana. The Statistical Package for Social Sciences version 25 was used to analyse the data. We found that 73.3% of parents/guardians would allow their children to be vaccinated against COVID-19. The binary logistic regression analysis shows that parents/guardians with Senior High School education, those who believed COVID-19 could not be cured, and those who agreed and those who neither agreed nor disagreed with the statement “once the vaccine is available and approved, it would be safe” were less likely to accept COVID-19 vaccine for their children. Also, parents/guardians who neither agreed nor disagreed that “the best way to avoid the complications of COVID-19 is by being vaccinated”, those who agreed that “I am of the notion that physiological/natural community is better compared to vaccine-induced immunity” and “I believe the vaccine programming may be likened to the new world order” were less likely to accept COVID-19 vaccine for their children. There is a need for public health practitioners to intensify education on the benefits and side effects of COVID-19 vaccines, as well as provide regular and up-to-date information about vaccines’ safety to parents and guardians.