Early identification of COVID-19 using a deep model trained on Chest X-Ray and CT images has gained considerable attention from researchers to speed up the process of identification of active COVID-19 cases. These deep models act as an aid to hospitals that suffer from the unavailability of specialists or radiologists, specifically in remote areas. Various deep models have been proposed to detect the COVID-19 cases, but few works have been performed to prevent the deep models against adversarial attacks capable of fooling the deep model by using a small perturbation in image pixels. This paper presents an evaluation of the performance of deep COVID-19 models against adversarial attacks. Also, it proposes an efficient yet effective Fuzzy Unique Image Transformation (FUIT) technique that downsamples the image pixels into an interval. The images obtained after the FUIT transformation are further utilized for training the secure deep model that preserves high accuracy of the diagnosis of COVID-19 cases and provides reliable defense against the adversarial attacks. The experiments and results show the proposed model prevents the deep model against the six adversarial attacks and maintains high accuracy to classify the COVID-19 cases from the Chest X-Ray image and CT image Datasets. The results also recommend that a careful inspection is required before practically applying the deep models to diagnose the COVID-19 cases.