One significant concern during the COVID-19 pandemic is parents’ mental health, which may consequently affect children’s health and well-being. The objective of this study is to investigate generalized anxiety and depression in parents of primary-school-aged children and identify risk factors for mental health problems. A cross-sectional survey comprising 701 parents of primary school children in five of Thailand’s major provinces was carried out from January to March 2022. Generalized anxiety and depression levels were assessed using the GAD-7 and PHQ-9. Logistic regression was performed to determine the effects of independent variables on anxiety and depression. Results showed that the prevalence of generalized anxiety and depression was 42.7% and 28.5%, respectively, among Thai parents. Three strong associative factors included: (1) having a youngest child with mental health problems; (2) not assisting their children every day; and (3) drinking alcohol. These findings show that the parents must deal with several difficulties when trying to maintain work and parenting duties while being confined at home during emergency situations. The government should provide sufficient assistance to parents who lack skills in handling children with emotional and behavioral problems. Meanwhile, health promotion to reduce alcohol consumption should continue to be an area of focus.