The outbreak of the COVID-19 pandemic is unarguably the biggest catastrophe of the 21st century, probably the most significant global crisis after the second world war. The rapid spreading capability of the virus has compelled the world population to maintain strict preventive measures. The outrage of the virus has rampaged through the healthcare sector tremendously. This pandemic created a huge demand for necessary healthcare equipment, medicines along with the requirement for advanced robotics and artificial intelligence-based applications. The intelligent robot systems have great potential to render service in diagnosis, risk assessment, monitoring, telehealthcare, disinfection, and several other operations during this pandemic which has helped reduce the workload of the frontline workers remarkably. The long-awaited vaccine discovery of this deadly virus has also been greatly accelerated with AI-empowered tools. In addition to that, many robotics and Robotics Process Automation platforms have substantially facilitated the distribution of the vaccine in many arrangements pertaining to it. These forefront technologies have also aided in giving comfort to the people dealing with less addressed mental health complicacies. This paper investigates the use of robotics and artificial intelligence-based technologies and their applications in healthcare to fight against the COVID-19 pandemic. A systematic search following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) method is conducted to accumulate such literature, and an extensive review on 147 selected records is performed.