Oliver Glasner's Eagles will take on Mikel Arteta's side at the Emirates Stadium at 19:30 GMT on Wednesday, 18th December.
The match will be broadcast live in the UK on Sky Sports.
Ticketing information will be announced via club channels in due course.
Palace have overcome Norwich City, Queens Park Rangers and Aston Villa to reach this stage of the competition – our first League Cup quarter-final since 2011/12, when Palace knocked out Manchester United at Old Trafford.
The Eagles last met Arsenal in the League Cup in 1992/93, when the North London side progressed through a two-legged semi-final.
Once again, any matches which end in a draw at this stage will go straight to penalties; extra-time is only used in the Carabao Cup from the semi-finals onwards.