A COVID-19 vaccine can be an important key for mitigating the spread of the pandemic, provided that it is accepted by a sufficient proportion of the population. This study investigated parents' intention to get vaccinated and to have one's child vaccinated against COVID-19. In May 2020, 612 parents participating with their child in the KUNO-Kids health study completed an online survey. Multivariable logistic regression models were calculated to analyze predictors of intention to vaccinate. Fifty-eight percent of parents intended to get vaccinated against COVID-19, and 51% intended to have their child vaccinated. Significant predictors for the intention to get vaccinated and for having the child vaccinated included stronger parental confidence in one's knowledge about prevention measures and lower beliefs that policy measures were exaggerated. Conclusion: COVID-19 vaccination hesitancy was considerable in our sample of parents in Germany. However, our study revealed some potentially modifiable factors which should be addressed by a comprehensive and tailored communication and education strategy. What is Known? A COVID-19 vaccine can mitigate the spread of the pandemic. Many parents are skeptical about vaccinations in general. What is New? COVID-19 vaccination hesitancy was considerable in our sample of parents from Germany, not only for getting vaccinated but also for having the child vaccinated. Negative parental attitudes regarding policy measures to contain the pandemic were associated with a lower intention to vaccinate.