The game will be played on Saturday January 8th subject to the demands of television.
The Sky Blues were ball number twelve and the drawing of 64 teams left in the competition was made by former Oasis guitarist and Specials fans Noel Gallagher and Kasabian's Serge Pizzorno at Wembley Stadium.
City will pick up £67,000 if they win the game.
The Sky Blues have only met Palace once in the FA Cup and that was back in 1908 when City lost 4-2 at Highfield Road.