The COVID-19 pandemic has impacted healthcare systems worldwide. Little is known about the impact of the pandemic on medical and psycho-social aspects of children with rare diseases such as pulmonary arterial hypertension and their parents. The study is based on children registered in The Database of Pulmonary Hypertension in the Polish Population and a parent-reported survey deployed during the first 6 months of the pandemic. The questionnaire consisted of six question panels: demographic data, fear of COVID-19, General Anxiety Disorder-7 (GAD-7), social impact of pandemic, patients’ medical status, and alarming symptoms (appearance or exacerbation). Out of 80 children registered, we collected 58 responses (72.5% response rate). Responders (parents) were mostly female (n = 55; 94.8%) at a mean age of 40.6 ± 6.9 years. Patients (children) were both females (n = 32; 55%) and males with a mean age of 10.0 ± 5.1 years. Eleven (19%) children had symptoms of potential disease exacerbation. Eight parents (72.7%) decided for watchful waiting while others contacted their GPs or cardiologists (n = 6; 54.5%). Three children had to be hospitalized (27.3%). Most planned hospitalizations (27/48; 56.2%) and out-patient visits (20/35; 57.1%) were cancelled, delayed, or substituted by telehealth services. Among the participating parents, the study shows very high levels of anxiety (n = 20; 34.5%) and concern (n = 55; 94.8%) and the need for detailed information (52; 89.6%) regarding COVID-19 and medical service preparedness during the pandemic. The COVID-19 pandemic has influenced child healthcare and caused high levels of anxiety among parents.