COVID-19 is a global infectious disease that can be easily spread by the contiguity of infected people. To prevent from COVID-19 and reduce its impact in sustainable smart cities, the global research communities are working relentlessly by harnessing the emerging technologies to develop the safest diagnosis, evaluation, and treatment procedures, and Internet of Things (IoT) is one of the pioneers among them. IoT can perform a pivotal role to diminish its immense contagious rate by suitable utilization in emerging healthcare IoT applications in sustainable smart cities. Therefore, the focus of this paper is to outline a survey of the emerging healthcare IoT applications practiced in the perspective of COVID-19 pandemic in terms of network architecture security, trustworthiness, authentication, and data preservation followed by identifying existing challenges to set the future research directions. The salient contributions of this work deal with the accomplishment of a detailed and comprehensive literature review of COVID-19 starting from 2019 through 2021 in the context of emerging healthcare IoT technology. In addition, we extend the correlated contributions of this work by highlighting the weak aspects of the existing emerging healthcare IoT applications, security of different network layers and secure communication environment followed by some associated requirements to address these challenges. Moreover, we also identify future research directions in sustainable smart cities for emerging healthcare IoT utilization in the context of COVID-19 with the most productive results and least network implementation costs.