This study examined effects of COVID-19 restrictions in early 2020 on movement (physical activity, sedentary behavior and sleep) and healthy eating behaviors in families with 0–12-year-old children in western Sydney, Australia. A total of 1,371 parents completed an online survey about changes in children's and families' food intake and movement behaviors. There was an increase in sedentary screen use by children (4.18/5.00) and families (3.91/5.00) and a slight increase in reported physical activity (3.56/5.00), amount of food consumed (3.58/5.00) and meals and snacks eaten (3.69/5.00) during the height of the COVID-19 restrictions compared to before. There was little change in reported sleep (3.17/5.00). Lower socioeconomic families were disproportionately affected, with greater increases in unhealthy eating (t = 2.739, P = 0.06), lower levels of improvement in physical activity, such as walking and cycling (t = −7.521, P < 0.001) and outdoor activity (t = 5.415, p < 0.001), and higher increases in family sedentary behavior (t = 2.313, P = 0.021). Therefore, even short periods of restrictions can result in detrimental health behavior changes. Such changes could become entrenched leading to increased risk of lifestyle diseases. Programmatic and policy strategies should be geared toward promoting healthy movement behaviors, focusing on families of lower socioeconomic status to ensure the pandemic does not widen an existing gap.