Background: Timely and precise identification of COVID-19 is an arduous task owing to the scarcity and inefficiency of the medical test kits. This has resulted in medical professionals turning towards Computed Tomography (CT) scans. Efforts are being made to design deep learning models capable of COVID-19 detection using CT scans. This has certainly reduced the manual intervention in disease detection but reported accuracy is limited. Methods: The present work proposes an automatic system for COVID-19 diagnosis based on deep features and Parameter Free BAT (PF-BAT) optimized Fuzzy K-nearest neighbor (PF-FKNN) classifier. Typically, features are extracted from the fully connected layer of transfer learned MobileNetv2 that are then employed for FKNN training. The hyper-parameters of FKNN are fine-tuned using PF-BAT. Results: The experimental results on the benchmark COVID CT scan data reveal that the proposed algorithm attains a validation accuracy of 99.38% which is better than the existing state-of-the-arts. Conclusion: The outcomes presented in the paper will aid in speedy detection of this virus at the different phases. Such a detection system will also increase the opportunities for fast recovery of patients worldwide thereby releasing the pressure off the medical professionals and the healthcare system around the world.