The outbreak of COVID-19 hit the world with an incomparable magnitude and introduced new challenges in the diagnosis and treatment of patients. Personal interactions have suddenly become dangerous which can be reduced by the use of digital technology in healthcare. Towards this, we have developed a low-cost remote vital sign monitoring system (VSM) that can be used at hospitals as well as at home for continuous and long-term monitoring of different clinical status, and provide extended support to the vulnerable patients. The proposed VSM has been designed with four layers: sensing layer, data processing layer, networking layer, and applications layer. It comes with three units: a wrist unit, a bedside monitor and a web-based graphical user interface (GUI) accessible by the nurse, physician or attendants remotely from anywhere. The effectiveness of measurement, transmission, and remote monitoring has been demonstrated by experiments. The system is designed with open source and low-cost hardware devices to ensure that it can be afforded and implemented in low resource settings of the developing countries. The proposed system can provide an effective way of delivering care to more patients while protecting everyone involved from infection.