ML algorithms are used to develop prognostic and diagnostic models and so to support clinical decision-making. This study uses eight supervised ML algorithms to predict the need for intensive care, intubation, and mortality risk for COVID-19 patients. The study uses two datasets: (1) patient demographics and clinical data (n = 11,712), and (2) patient demographics, clinical data, and blood test results (n = 602) for developing the prediction models, understanding the most significant features, and comparing the performances of eight different ML algorithms. Experimental findings showed that all prognostic prediction models reported an AUROC value of over 0.92, in which extra tree and CatBoost classifiers were often outperformed (AUROC over 0.94). The findings revealed that the features of C-reactive protein, the ratio of lymphocytes, lactic acid, and serum calcium have a substantial impact on COVID-19 prognostic predictions. This study provides evidence of the value of tree-based supervised ML algorithms for predicting prognosis in health care.