With implemented school closures, the global crisis of COVID-19 has caused drastic changes in the dynamics and routines of children and their families. The rapid transition to homeschooling and social distancing measures have been particularly challenging for schoolchildren and their parents. In the adverse situation of COVID-19, children are more vulnerable to contextual factors such as familial risks, leading to unfavorable outcomes in children’s mental health, their emotional and psychosocial development. The present study aimed to synthesize available literature on psychosocial outcomes in schoolchildren (ages 6–13 years) who were exposed to family-related stressors during mandatory school closures. A systematic review was carried out, following the PRISMA guideline. A total of 419 records were retrieved from electronic databases, journals, and reference lists of primary studies and reviews. Studies were analyzed by the interrelation of negative child outcomes and parent-related variables during the period of school closure. Ten studies were included in this review. Studies varied in quality, in the combination of psychosocial factors, and child outcomes. Identified psychosocial variables impacting children included parental mental health, parental stress, parent-child interaction, and parenting stress. Identified negative outcomes in children encompassed emotional problems, behavioral problems, hyperactivity, anxiety and depression. Overall, results highlighted the link between children’s psychological response and parent-related variables during school closures. Results show that pandemic-related school closures had a considerable effect on children. However, findings cannot be interpreted conclusive as studies measured other factors, that contributed to a child’s psychological status quo.