The ECB announced last week that no professional cricket would be played in England and Wales until July 1 at the earliest due to the Covid-19 pandemic, with the Blast likely to be pushed back to the final months of the season.
Surrey said in a statement: "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."
The club had previously cancelled Michael Neser's contract, following the initial suspension of the first seven rounds of County Championship fixtures.
Both players were also due to play in the inaugural season of the Hundred, which has been pushed back to 2021.
Alec Stewart, Surrey's director of cricket, said: "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.
"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."