The Coronavirus Disease 2019 (COVID-19) global pandemic has threatened the lives of people worldwide and poses considerable challenges. Early and accurate screening of infected people is vital for combating the disease. To help with the limited quantity of swab tests, we propose a machine learning prediction model to accurately diagnose COVID-19 from clinical and/or routine laboratory data. The model exploits a new ensemble-based method called the deep forest (DF), where multiple classifiers in multiple layers are used to encourage diversity and improve performance. The cascade level employs the layer-by-layer processing and is constructed from three different classifiers: extra trees, XGBoost, and LightGBM. The prediction model was trained and evaluated on two publicly available datasets. Experimental results show that the proposed DF model has an accuracy of 99.5%, sensitivity of 95.28%, and specificity of 99.96%. These performance metrics are comparable to other well-established machine learning techniques, and hence DF model can serve as a fast screening tool for COVID-19 patients at places where testing is scarce.