The T20 Blast was scheduled to start on May 28 but it has been postponed following the ECB's announcement that no professional cricket would be played in England and Wales until July 1 in view of the pandemic.
"Given the postponement of (the Blast) and the current uncertainty around the makeup of the domestic season ... it was mutually agreed that the players' contracts would be cancelled," Surrey said in a statement.
Additionally, both Shadab and Short were due to feature in the inaugural season of the Hundred, which was also postponed to 2021 due to the global health crisis.
"I would like to thank both Shadab & D'Arcy and their management companies for their understanding of the current situation and the impact these testing times are having on our game," Alec Stewart, Surrey's director of cricket, said.
"While we continue to prepare for cricket at The Kia Oval this summer, uncertainties around restrictions and scheduling across the world and here in the UK means this is the most sensible decision for both the players and the club for now."
Several counties such as Yorkshire, Kent, Lancashire, Gloucestershire and Hampshire were forced to cancel contracts of their overseas players, including Indian cricketers Cheteshwar Pujara and R Ashwin.