In December 2019 a highly infectious virus named 'Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-COV-2) sparked a global pandemic. Deep Neural Networks have been extensively used to develop intelligent systems for accurate and timely diagnosis of COVID-19 infection using chest Computerized Tomography. However, Deep Learning approaches require a large annotated dataset. The fundamental goal of this research is to develop a model that would learn efficiently from a size-limited dataset. This study proposes a hybrid feature extraction approach. Our proposed technique exploits the CT imaging characteristics of COVID-19 infection through hand-crafted texture features and complex features extracted by a pre-trained ResNet101 network. The 7-layered Deep Convolutional Neural Network used for classification is optimized using a revolutionary rapid navigation optimization technique. The proposed optimization improves the Moth-Flame Optimizer by integrating the concept of Mayfly velocity to update the position of the Moth fly in the exploration space. When tested on an open access dataset, COVID -CT containing 349 COVID-19 positive CT images and 397 COVID-19 negative CT images, the accuracy, sensitivity, and specificity of the proposed rapid navigation optimization-based deep CNN classifier were 97.260%, 94.301%, and 99%, respectively. The proposed model was also tested on an augmented COVID -CT dataset and a larger dataset, COVIDx-CT-3A. The proposed model has exhibited an accuracy of 99.61% and 89.35% on the augmented COVID -CT dataset and COVIDx-CT-3A, respectively. Our proposed method outperformed the other published cutting-edge research works that have tested on the small COVID -CT dataset.