Patients with infectious diseases are often at increased risk of anxiety during treatment. The prevalence of anxiety and depression in infected people increased significantly during the COVID-19 pandemic, and the risk factors for these mental health problems need to be urgently investigated. In this study, a cross-sectional study was conducted in Shanghai in 2022, which included 1283 patients and systematically assessed their sociodemographic characteristics and mental health status. A random forest classifier combined with the Boruta algorithm was used to screen predictors, and a nomogram was constructed based on the screening results. The results of the study showed that entrapment (OR 1.07, 95% CI 1.05-1.09, P < 0.001), defeat (OR 1.04, 95% CI 1.01-1.07, P < 0.01) and stigma (OR 1.05, 95% CI 1.03-1.06, P < 0.001) were positively associated with anxiety, whereas social support (OR 0.97, 95% CI 0.96-0.98, P < 0.001) was negatively associated with anxiety. The C-index of the model was 0.858, the area under the ROC curve (AUC) was 0.861 (95% CI 0.834-0.888), and the P value of the Hosmer-Lemeshow test was 0.07, indicating that the model fit well. Based on the Random Forest machine learning method, this study successfully constructed a prediction model for anxiety risk in COVID-19 patients, screening out key risk factors such as feeling trapped, frustration, stigma and social support, providing a scientific basis for clinical practice and public health, and helping to promote personalized interventions for anxiety and the building of a mental health support system.