It will be the first time the two sides have met since they were both in the old Second Division in the 1990/91 season.
Over the years City have fared well against the Midlands side, and have only lost 4 out of the 28 meetings at Boothferry Park.
Tigers manager Jan Molby said: "It's a great draw for the club in commercial terms and also gives our lads the chance to pit their wits against what are effectively Premiership players.
"We will go into the game looking for a victory but it'll be extremely tough and they will take some beating."
Meanwhile the draw for the Worthington Cup has picked out some good derbies for the First Round. Burnley v Blackpool is set to be a great Lancashire derby. Meanwhile Mansfield play Derby, Crewe go to Port Vale, and Watford play Luton.
Boston United play Bristol Rovers in a preliminary round, with the winner getting Cardiff at home in the First Round Proper. The qualifying match is required as Division One side Ipswich Town could be in Europe, and would be entitled to a bye to the Third Round.
Preliminary Round (Tuesday 20th August)
Bristol Rovers v Boston United
First Round (Tuesday 9th/Wednesday 10th September)
Huddersfield Town v Darlington
Rotherham United v Carlisle United
Lincoln City v Stockport County
Wrexham v Bradford City
Grimsby Town v Chesterfield
Northampton Town v Wigan Athletic
Mansfield Town v Derby County
Oldham Athletic v Notts County
Sheffield United v York City
Preston North End v Scunthorpe United
Hull City v Leicester City
Hartlepool United v Tranmere Rovers
Nottingham Forest v Kidderminster Harriers
Burnley v Blackpool
Bury v Stoke City
Port Vale v Crewe Alexandra
Macclesfield Town v Barnsley
Sheffield Wednesday v Rochdale
Bristol City v Oxford United
Swindon Town v Wycombe Wanderers
Walsall v Shrewsbury Town
Rushden & Diamonds v Millwall
Leyton Orient v Queens Park Rangers
Cambridge United v Reading
Torquay United v Gillingham
Watford v Luton Town
AFC Bournemouth v Brentford
Bristol Rovers or Boston United v Cardiff City
Norwich City v Cheltenham Town
Brighton & Hove Albion v Exeter City
Crystal Palace v Plymouth Argyle
Swansea City v Wolverhampton Wanderers
Coventry City v Colchester United
Portsmouth v Peterborough United
Southend United v Wimbledon