The tie will see former Leeds midfielder Shaun Derry up against his former team mates at Elland Road.
Palace got through the first round for the first time since 2005 on Tuesday night with a 2-1 win against Hereford.
Matches are due to take place week commencing August 25 except Manchester City, due to European commitments.
Full second round draw;
Ipswich Town v Colchester United
Coventry City v Newcastle United
Hartlepool United v West Bromwich Albion
West Ham United v Macclesfield Town
Huddersfield Town v Sheffield United
Cardiff City v MK Dons
Swansea City v Hull City
Rotherham United v Wolverhampton Wanderers
Brighton and Hove Albion v Manchester City
Reading v Luton Town
Blackburn Rovers v Grimsby Town
Wigan Athletic v Notts County
Leeds United v Crystal Palace
Crewe Alexandra v Bristol City
Middlesbrough v Yeovil Town
Fulham v Leicester City
Queens Park Rangers v Carlisle United
Nottingham Forest v Sunderland
Burnley v Oldham Athletic
Southampton v Birmingham City
Bolton Wanderers v Northampton Town
Watford v Darlington
Preston North End v Derby County
Cheltenham Town v Stoke City