(1) Background: Understanding oral health needs and barriers is important to overcome the oral disease burden, especially after the COVID-19 pandemic. The aim of this study was to assess oral health needs and barriers among Saudi children after the COVID-19 pandemic wave started. (2) Methods: Parents of healthy children aged 3–11 years from five regions of Saudi Arabia were surveyed using an electronically administered validated questionnaire from Febuary-2021 to July-2021. Oral lesions/manifestations during the last 12 months reported by parents included tooth discoloration, ulcers, abscess, swelling of the gingiva, halitosis, gingival bleeding, dry mouth, pain while eating, difficulty in speaking or eating, burning sensation, and white spots. Barriers were assessed according to the WHO Oral Health Questionnaire. (3) Results: Children experiencing toothaches were reported by 1098 (72.4%) respondents. When reported, oral manifestations and lesions were associated with a higher inability to visit a dentist (p < 0.001). Barriers to dental care were more frequent among parents with lower education (p < 0.001; adjusted-odds ratio (AOR), 1.815) and a greater number of children (p < 0.001; AOR, 1.197). (4) Conclusion: Parents reported a high frequency of unmet oral health needs. Education could play an important role in improving oral health care in children and as a predictor of public health concerns.