Measures taken to contain the COVID-19 pandemic are particularly stressful for families. Limited data is available regarding the effects of a mandatory quarantine on the psychological stress of children, adolescents and their parents. Quarantined individuals participating in the online-based CoCo-Fakt study had at least one child n = 2153). Parents were asked about how often their children felt nervous, anxious, or tense, down or depressed, lonely or physical reactions occur. A relative sum score characterizing psychosocial stress was determined and related to parents’ socio-demographic factors, psychosocial distress, coping strategies and resilience. Parents reported significantly higher psychological stress if at least one child was quarantined. Parents’ relative psychological stress sum score had the strongest influence on the psychological state of the children across all age groups (β = 0.315–0.457) besides male sex of the reporting parent, no partnership, low to medium socioeconomic status, lower resilience and coping scores, and parents quarantined as close contacts. The variance in the linear regression models was between 17.8% and 31.4%. These findings highlight that the entire family system must be considered during official mandatory quarantines.