The natural disasters created by infectious diseases have a formidable impact on people and societies. Without affecting the city infrastructure, pandemics leave the places abandoned because of the shortage of human resources, either due to deaths, illness, or unwillingness to work because of health risks. However, providing a timely response can prevent losses from occurring due to the virus dissemination. Since the first reported case of influenza in 1918 to the current pandemic Coronavirus Disease-2019 (COVID-19), the system playing a key role in saving human lives is healthcare. Nowadays, smart healthcare system development is a popular trend and wireless communication is the backbone of such systems. To provide patients with diagnosis, treatments, and several health services both within hospitals and remotely, all the healthcare units must be equipped with advanced technologies. A rapid response unit is also required to handle the thrust of the patients and queries generated during disasters. This paper discusses healthcare communication challenges and possible solutions for early awareness and rapid response in disaster situations under the human-centric vision of sixth-generation wireless technologies.