Championship side to visit Fratton
Ticket information and date/kick-off time will be announced in due course.
The sides have not met since they were both in the second tier during the 2011/12 campaign.
Derby did the double over the Blues that season, including a 2-1 triumph at Fratton Park.
There have been four previous clashes in the League Cup – in 1961, 1963, 1974 and 1994 – with two victories apiece.
Derby, meanwhile, saw off Carlisle, Charlton, Reading and Fulham on their way to the quarter-finals, where they were beaten by eventual winners Chelsea.
Capital One Cup first round draw
Carlisle United v Chesterfield
Nottingham Forest v Walsall
Fleetwood Town v Hartlepool United
Scunthorpe United v Barnsley
Bolton Wanderers v Burton Albion
Accrington Stanley v Hull City
Rochdale v Coventry City
Oldham Athletic v Middlesbrough
Huddersfield Town v Notts County
Blackburn Rovers v Shrewsbury Town
Morecambe v Sheffield United
Doncaster Rovers v Leeds United
Wigan Athletic v Bury
Northampton Town v Blackpool
Sheffield Wednesday v Mansfield Town
Rotherham United v Cambridge United
Crewe Alexandra v Preston North End
York City v Bradford City
Port Vale v Burnley
Peterborough United v Crawley Town
Yeovil Town v Queens Park Rangers
Plymouth Argyle v Gillingham
Swindon Town v Exeter City
Bristol Rovers v Birmingham City
Ipswich Town v Stevenage
Luton Town v Bristol City
Charlton Athletic v Dagenham & Redbridge
Wolverhampton Wanderers v Newport County
Brentford v Oxford United
POMPEY v Derby County
Southend United v Brighton & Hove Albion
Milton Keynes Dons v Leyton Orient
Cardiff City v AFC Wimbledon
Millwall v Barnet
Wycombe Wanderers v Fulham
Colchester United v Reading