Low copeptin levels may indicate inadequate arginine-vasopressin release promoting arterial hypotension, whereas high copeptin concentrations may reflect disease severity. This single-center prospective non-randomized clinical trial analyzed the course of blood copeptin in critically ill normo- and hypotensive children and its association with disease severity. In 164 patients (median age 0.5 years (interquartile range 0.1, 2.9)), the mean copeptin concentration at baseline was 43.5 pmol/L. Though not significantly different after 61 h (primary outcome, mean individual change: −12%, p = 0.36, paired t-test), we detected 1.47-fold higher copeptin concentrations during arterial hypotension when compared to normotension (mixed-effect ANOVA, p = 0.01). In total, 8 out of 34 patients (23.5%) with low copeptin concentrations <10 pmol/L were hypotensive. Copeptin was highest in the adjusted mixed-effect regression analysis within the first day (+20% at 14 h) and decreased significantly at 108 h (−27%) compared to baseline (p = 0.002). Moreover, we found a significant association with vasopressor-inotrope treatment intensity, infancy (1–12 months) and cardiopulmonary bypass (all p ≤ 0.001). In conclusion, high copeptin values were associated with arterial hypotension and severity of disease in critically ill children. This study does not support the hypothesis that low copeptin values might be indicative of arginine-vasopressin deficiency.