Palace enter the historic competition in the Third Round proper, alongside other Premier League and Championship sides.
Their knock-out clash will be played on Friday, 11th December at 19:00 GMT.
If drawn, the match will go to extra time and penalties. The Youth Cup final will be held on Saturday, 24th April, 2021.
The game with Tottenham Hotspur initially scheduled for December 12th will now be played on December 5th at 11am.
Last season, Palace bowed out against Wolverhampton Wanderers after a spirited clash in the cup they famously won in both 1977 and 1978. So far this season, Paddy McCarthy's Under-18s have won six of their seven games, beating 2018 Youth Cup champions Chelsea in October.
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