Objectives The ideal time for nasoalveolar molding (NAM) of infants with cleft lip and/or palate (CLP) is the first weeks after birth. The burden and responsibility that this method of treatment imposes on parents may result in incompliance. The coronavirus (COVID-19) pandemic and the redirection of health resources can make the situation worse. Therefore, this study evaluated the anxiety, complications, and incompliance of parents undergoing NAM during the COVID-19 pandemic. Materials and methods Demographic data of 35 infants with CLP treated during the COVID-19 pandemic, compliance and level of anxiety of both parents in addition to their complications were reported. The association between different variables and incompliance was evaluated by simple and multiple logistic regressions. The level of significance was considered at P value less than 0.05. Results The highest level of parental anxiety related to the NAM process was the delay in ending the treatment. Meanwhile, the reason for the highest level of anxiety related to attending the treatment sessions was the probability of the infant's COVID-19 infection. Fathers expressed lower levels of anxiety than mothers, significantly. The most prevalent NAM complication was skin irritation. Parents of younger infants (≤28 days) and those with a history of COVID-19 infection were more compliant. Conclusions COVID-19 pandemic caused a significant increase in the level of anxiety in both parents, mainly due to the delay in treatment ending and the possibility of infant's infection. Moreover, considering the importance of treatment time, parents of younger infants were more compliant with the NAM process.