In March 2020, the Italian Government imposed mandatory home confinement to limit the spread of COVID-19. Few studies assessed the psychophysical impact of COVID-19 on chronically ill children. This study examined these effects on children with Type 1 Diabetes Mellitus (T1D) and their caregivers. Seventy-one patients (7–13 years) with T1D and their caregivers were administered a survey created ad hoc and some standardized questionnaires, assessing psychological well-being and anxiety. Medical data (physical and biochemical characteristics) were recorded before (T₀, January–February) and after (T₁, May–June) the lockdown. Paired Student t-test, Spearman two-tailed correlations, and a linear regression model were used for statistical analysis. Children at T₁ showed higher BMI (body mass index), daily total and basal insulin dose, and time spent in therapeutic range, and they showed lower HbA1c (glycated hemoglobin), time spent above the therapeutic range, and standard deviations of the mean glucose values than at T₀. A total of 32.9% scored in the clinical range for separation anxiety. The increase in separation anxiety was predicted by younger age, female gender, more recent T1D diagnosis, less time spent in therapeutic range at T₁, and higher perceived fear of COVID-19 infection. In a pandemic context, separation anxiety may be stronger in younger females, with more recent T1D diagnosis and poor metabolic control, thus affecting the parent’s ability to manage diabetes and to support children’s autonomy.