Chest computer tomography (CT) provides a readily available and efficient tool for COVID-19 diagnosis. Wavelet and contourlet transforms have the advantages of being localized in both space and time. In addition, multiresolution analysis allows for the separation of relevant image information in the different subbands. In the present study, transform-based features were investigated for COVID-19 classification using chest CT images. Several textural and statistical features were computed from the approximation and detail subbands in order to fully capture disease symptoms in the chest CT images. Initially, multiresolution analysis was performed considering three different wavelet and contourlet levels to determine the transform and decomposition level most suitable for feature extraction. Analysis showed that contourlet features computed from the first decomposition level (L1) led to the most reliable COVID-19 classification results. The complete feature vector was computed in less than 25 ms for a single image having of resolution 256 × 256 pixels. Next, particle swarm optimization (PSO) was implemented to find the best set of L1-Contourlet features for enhanced performance. Accuracy, sensitivity, specificity, precision, and F-score of a 100% were achieved by the reduced feature set using the support vector machine (SVM) classifier. The presented contourlet-based COVID-19 detection method was also shown to outperform several state-of-the-art deep learning approaches from literature. The present study demonstrates the reliability of transform-based features for COVID-19 detection with the advantage of reduced computational complexity. Transform-based features are thus suitable for integration within real-time automatic screening systems used for the initial screening of COVID-19.