Investigating the epidemiology of mental health disorders resulting from COVID-19 intervention measures, primary school closures, and social isolation in children and adolescents needs to be prioritized over adults at the post-pandemic stage. Most preliminary psychosocial studies conducted during the pandemic have demonstrated that younger age groups are the most vulnerable to such implications. Thus, this study aims to estimate the probable prevalence of specific anxiety disorders in children and quantify their relationships with relevant demographic risk factors. We used a cross-sectional study comprising 430 children aged between 8- and 18 years old living in Kuwait during the period of school closures as well as full and partial lockdowns. The survey included questions about participants' characteristics, children's anxiety using the Screen for Child Anxiety Related Emotional Disorders Questionnaire (SCARED) scale, and children's emotions and behaviours using the Strengths and Difficulties Questionnaire (SDQ). Univariate and multivariate logistic regression analyses were used to summarize the demographic and characteristics of the participants and their association with general, social, and generalized anxieties, as well as behavioural and emotional difficulties. We inferred that 24.83% of our participants had at least one anxiety disorder, while 20.19% were classified as abnormal on the SDQ scale. Our multivariate analysis revealed that lockdown duration and sex of the child were consistently significant predictors (p-values < 0.05) of the broad spectrum of selected mental disorders. Additionally, we inferred notable increases in the likelihood of mental disorders associated with the increased duration of lockdowns. Our findings revealed preliminary insights into the vulnerability of young populations to the indirect negative impacts of strict public health measures during pandemic emergencies. Thus, authorities should consider such implications when planning and implementing similar interventions in future pandemics.