Since December 2019, the coronavirus disease (COVID-19) outbreak has caused many death cases and affected all sectors of human life. With gradual progression of time, COVID-19 was declared by the world health organization (WHO) as an outbreak, which has imposed a heavy burden on almost all countries, especially ones with weaker health systems and ones with slow responses. In the field of healthcare, deep learning has been implemented in many applications, e.g., diabetic retinopathy detection, lung nodule classification, fetal localization, and thyroid diagnosis. Numerous sources of medical images (e.g., X-ray, CT, and MRI) make deep learning a great technique to combat the COVID-19 outbreak. Motivated by this fact, a large number of research works have been proposed and developed for the initial months of 2020. In this paper, we first focus on summarizing the state-of-the-art research works related to deep learning applications for COVID-19 medical image processing. Then, we provide an overview of deep learning and its applications to healthcare found in the last decade. Next, three use cases in China, Korea, and Canada are also presented to show deep learning applications for COVID-19 medical image processing. Finally, we discuss several challenges and issues related to deep learning implementations for COVID-19 medical image processing, which are expected to drive further studies in controlling the outbreak and controlling the crisis, which results in smart healthy cities.