This study aimed to investigate the emotional and behavioral responses of children with neurodevelopmental disorders and their parents during the recent novel coronavirus disease (COVID-19) pandemic and the associated factors. Our study included 299 children and adolescents with neurodevelopmental disorders and 299 mothers or fathers. Participant groups were as follows: autism spectrum disorder (n = 131, 43.8%); intellectual disability (n = 103, 34.4%); specific learning disorder (n = 46, 15.4%); and communication disorder (n = 19, 6.4%). A data form was created to investigate the emotional, behavioral, sleep problems, and appetite changes of the cases, and it was adapted for online application and conveyed to the parents in the form of emails. Our study indicated that children and adolescents' emotional problems were 44.5%, behavioral problems 33.4%, sleep problems 65.2%, and appetite problems 32.4%. Irritability (35.5%), hyperactivity (37.8%), stereotyped behavior (29.8%), delayed sleep phase (51.5%) were the most common problems reported by the parents. The frequencies of emotional and behavioral problems in the ASD group were higher than in the other groups (p < 0.05). In addition, the Hospital Anxiety Depression Scale (HADS) was used to determine the parents' anxiety and depression symptoms. Mean HADS anxiety and depression scores of parents were 8.5 ± 4.3 and 7.8 ± 4.2, respectively. Our study demonstrated that the COVID-19 pandemic and lockdown negatively affected children with neurodevelopmental disorders and their parents in many areas. It is necessary that these children and their families are evaluated and supported by local professionals, as the ongoing pandemic can exacerbate the current challenges. The findings of our study reflect the early period of the pandemic. For this reason, longitudinal studies about the long-term consequences of the pandemic are needed.