To clarify the physical and mental conditions of children during the coronavirus disease 2019 pandemic and consequent social distancing in relation to the mental condition of their caregivers. This internet-based nationwide cross-sectional study was conducted between April 30 and May 13, 2020. The participants were 1,200 caregivers of children aged 3-14 years. Child health issues were categorized into "at least one" or "none" according to caregivers' perception. Caregivers' mental status was assessed using the Japanese version of the Kessler Psychological Distress Scale-6. The association between caregivers' mental status and child health issues was analyzed using logistic regression models. Among the participants, 289 (24.1%) had moderate and 352 (29.3%) had severe mental distress and 69.8% of children in their care had health issues. The number of caregivers with mental distress was more than double that reported during the 2016 national survey. After adjusting for covariates, child health issues increased among caregivers with moderate mental distress (odds ratio 2.24, 95% confidence interval 1.59-3.16) and severe mental distress (odds ratio 3.05, 95% confidence interval 2.17-4.29) compared with caregivers with no mental distress. The results highlight parents' psychological stress during the pandemic, suggesting the need for adequate parenting support. However, our study did not consider risk factors of caregivers' mental distress such as socioeconomic background. There is an urgent need for further research to identify vulnerable populations and children's needs to develop sustainable social support programs for those affected by the outbreak.