Our aim was to compere diabetes-related distress (DD) in young patients with type 1 diabetes mellitus (T1DM) and in their parents before and during the national COVID-19-related lockdown when schools operated on-line. Problems Areas in Diabetes-Child (PAID-Ch), Teen (PAID-T) and Parent (P-PAID-Ch, P-PAID-T) questionnaires in paper version were used to evaluate DD before COVID-19 pandemic (November 2019–February 2020) and during the lockdown (April 2020) the same surveys were performed by phone. We enrolled 76 patients (median age (Q1–Q3): 13.6 (11.8–15.2) years; 21 children, 55 adolescents; T1DM duration 3.7 (1.7–6.8) years). Initial PAID score was lower in teenage boys than in girls (34.0 (24.0–42.0) vs. 44.5 (40.0–50.5), p = 0.003). In teens PAID score decreased significantly during the lockdown (−3.0 (−11.0–3.0), p = 0.018), more in girls than boys (p = 0.028). In children (−3.0 (−14.0–7.0), p = 0.131) and parents PAID did not change (teens’ parents: 3.0 (−9.0–10.0), p = 0.376; children’s parents: −5.0 [−9.0–1.0], p = 0.227). In the studied group COVID-19 pandemic-related lockdown was associated with decrease in DD in teens with T1DM, particularly in girls, while no significant change in DD was observed in children or parents. DD decrease in teens during the pandemic should attract attention to the potential “rebound” of DD related to return to regular on-site school routine.