As a multidimensional and universal stressor, the COVID-19 pandemic negatively affected the mental health of children, adolescents, and adults worldwide. In particular, families faced numerous restrictions and challenges. From the literature, it is well known that parental mental health problems and child mental health outcomes are associated. Hence, this review aims to summarize the current research on the associations of parental mental health symptoms and child mental health outcomes during the COVID-19 pandemic. We conducted a systematic literature search in Web of Science (all databases) and identified 431 records, of which 83 articles with data of over 80,000 families were included in 38 meta-analyses. A total of 25 meta-analyses resulted in significant small to medium associations between parental mental health symptoms and child mental health outcomes (r = 0.19 to 0.46, p < 0.05). The largest effects were observed for the associations of parenting stress and child mental health outcomes. A dysfunctional parent–child interaction has been identified as a key mechanism for the transmission of mental disorders. Thus, specific parenting interventions are needed to foster healthy parent–child interactions, to promote the mental health of families, and to reduce the negative impacts of the COVID-19 pandemic.