To investigate the prevalence of emotional and behavioral problems (EBPs) among children during the COVID-19 post-pandemic in China; examine associations between COVID-19-related knowledge and precautions and problems in children, and explore the potential explanatory value of the mental health status of caregivers on any associations observed. Based on a cross-sectional design, caregivers of 6,017 children from 12 primary schools in Shanghai and Taizhou, China, were invited to complete an online survey from June 26 to July 6, 2020. EBPs of the children were assessed using the Strengths and Difficulties Questionnaire (SDQ), while the emotional problems of caregivers were assessed using the Depression Anxiety Stress Scales-21 (DASS-21). Structural equation modeling was employed to estimate the direct and indirect associations (explained by the emotional problems of caregivers) between COVID-19-related knowledge and precautions and the EBPs among children. The overall prevalence of EBPs in the sample was 12.5%, and 5.3% of them had a high or very high SDQ total difficulties score during the COVID-19 post-pandemic. After adjustment for covariates, higher COVID-19-related knowledge (β = −0.83;P< 0.001) and precautions (β = −0.80;P< 0.001) were significantly associated with lower SDQ total difficulties score among children. There was an explanatory effect of emotional problems of caregivers on the aforementioned associations, which explained 31% and 41% of the total effect, respectively. Higher levels of knowledge and precautions of COVID-19 were associated with lower EBPs among children, and the relationship was partially explained by the emotional problems in caregivers. It may be beneficial to improve pandemic-related prevention education and adopt psychological interventions toward the emotional status of caregivers for the psychological health of children.