Objective The COVID-19 outbreak has negatively affected children in many ways. This study aimed to compare the psychological responses of children exposed to different levels of stress during the COVID-19 outbreak. Methods The anxiety levels, negative thoughts, and quality of life of COVID-19-positive children with COVID-19-positive parents (Child+ group, n=17), COVID-19-negative children who are separated from COVID-19-positive parents (Parent+ group, n=59), and a control group (n=64) were compared. The participants completed the Screen for Child Anxiety and Related Disorders (SCARED), Children’s Negative Cognitive Errors Questionnaire (CNCEQ), and Pediatric Quality of Life Inventory (PedsQL). Results The statistical analysis revealed that the Parent+ group recorded higher SCARED and CNCEQ scores and lower PedsQL scores in comparison with the control group. No statistically significant difference was found between the scores of the Child+ and control groups. Furthermore, high CNCEQ scores and low PedsQL scores in the Parent+ group predicted an increase in their SCARED scores. Conclusion Our study indicates that separating children from their parents during the COVID-19 outbreak negatively influences their mental health and increases their anxiety levels.