Early detection and diagnosis of COVID-19, as well as the exact separation of non-COVID-19 cases in a non-invasive manner in the earliest stages of the disease, are critical concerns in the current COVID-19 pandemic. Convolutional Neural Network (CNN) based models offer a remarkable capacity for providing an accurate and efficient system for the detection and diagnosis of COVID-19. Due to the limited availability of RT-PCR (Reverse transcription-polymerase Chain Reaction) tests in developing countries, imaging-based techniques could offer an alternative and affordable solution to detect COVID-19 symptoms. This paper reviewed the current CNN-based approaches and investigated a custom-designed CNN method to detect COVID-19 symptoms from CT (Computed Tomography) chest scan images. This study demonstrated an integrated method to accelerate the process of classifying CT scan images. In order to improve the computational time, a hardware-based acceleration method was investigated and implemented on a reconfigurable platform (FPGA). Experimental results highlight the difference between various approximations of the design, providing a range of design options corresponding to both software and hardware. The FPGA-based implementation involved a reduced pre-processed feature vector for the classification task, which is a unique advantage of this particular application. To demonstrate the applicability of the proposed method, results from the CPU-based classification and the FPGA were measured separately and compared retrospectively.