Coronavirus disease 2019, i.e. COVID-19 has imposed the public health measure of keeping social distancing for preventing mass transmission of COVID-19. For monitoring the social distancing and keeping the trace of transmission, we are obligated to develop various types of digital surveillance systems, which include contact tracing systems and drone-based monitoring systems. Due to the inconvenience of manual labor, traditional contact tracing systems are gradually replaced by the efficient automated contact tracing applications that are developed for smartphones. However, the commencement of automated contact tracing applications introduces the inevitable privacy and security challenges. Nevertheless, unawareness and/or lack of smartphone usage among mass people lead to drone-based monitoring systems. These systems also invite unwelcomed privacy and security challenges. This paper discusses the recently designed and developed digital surveillance system applications with their protocols deployed in several countries around the world. Their privacy and security challenges are discussed as well as analyzed from the viewpoint of privacy acts. Several recommendations are suggested separately for automated contact tracing systems and drone-based monitoring systems, which could further be explored and implemented afterwards to prevent any possible privacy violation and protect an unsuspecting person from any potential cyber attack.