Dental fear and anxiety is a significant issue that affects pediatric patients and creates challenges in oral health management. Considering that the coronavirus disease 2019 (COVID-19) pandemic, along with its associated sanitary regime, social distancing measures and nationwide quarantines, could itself induce public fears, including in children, it is of great interest to explore whether this situation and the necessity of reorganizing dental care could potentially affect the emotional state of pediatric patients facing a need for urgent dental intervention. The present study assessed the emotional state of children ≤ seven years old (n = 25) requiring dental healthcare during a nationwide quarantine in Poland, as well as the anxiety levels of their caregivers. The Faces Anxiety Scale was adopted, and the evaluation was independently performed by the dentist, caregivers and children themselves. The level of anxiety in caregivers was also measured. As demonstrated, children requiring dental intervention during the nationwide quarantine did not reveal a significantly higher anxiety level as compared to the age- and indication-matched pre-pandemic control group (n = 20), regardless of whether their emotional state was evaluated by the dentist, caregivers, or by themselves. However, the share of children scoring the lowest anxiety level in all assessments was smaller in the pandemic group. Boys in the pandemic group had a higher anxiety level, as indicated by a caregiver assessment, and displayed a negative correlation with age in all three types of evaluation. Moreover, caregiver anxiety levels were higher in the pandemic group as compared to the pre-pandemic subset and revealed stronger correlations with the dental anxiety in children. The results suggest that the reorganization of oral healthcare under the pandemic scenario did not have a profound effect on children’s dental anxiety. Nevertheless, findings in young boys highlight that they may be more vulnerable and require special care to mitigate their anxiety and decrease the risk of dentophobia in the future—these observations must be, however, treated with caution due to the small sample size and require further confirmation. Moreover, it is important to reassure caregivers of the safety of the dental visit during the pandemic to minimize the effect of their own anxiety on dental fears in children.