The last meeting between the two side was also in the first round of the League Cup at Gresty Road in 2008 when Barnsley lost 2-0.
Crewe manager, Steve Davis, is a former Barnsley player having made 119 appearances for the Reds in the 1990s.
Overall Barnsley have won 23 of their head-to-heads with Crewe winning just 12 times. Fifteen matches have ended in a draw.
Ties will be played in the week commencing 11th August 2014.
The full draw is:
Oldham Athletic v Middlesbrough
Shrewsbury Town v Blackpool
Sheffield Wednesday v Notts County
Tranmere Rovers v Nottingham Forest
Leeds United v Accrington Stanley
Bolton Wanderers v Bury
Rochdale v Preston North End
Rotherham United v Fleetwood Town
Carlisle United v Derby County
Port Vale v Hartlepool United
Morecambe v Bradford City
Barnsley v Crewe Alexandra
Chesterfield v Huddersfield Town
Blackburn Rovers v Scunthorpe United
Burton Albion v Wigan Athletic
York City v Doncaster Rovers
Sheffield United v Mansfield Town
Reading v Newport County
Bristol City v Oxford United
Brighton & Hove Albion v Cheltenham Town
Coventry City v Cardiff City
Luton Town v Swindon Town
Dagenham & Redbridge v Brentford
Charlton Athletic v Colchester United
Crawley Town v Ipswich Town
Wolverhampton Wanderers v Northampton Town
Yeovil Town v Gillingham
Milton Keynes Dons v AFC Wimbledon
Exeter City v AFC Bournemouth
Stevenage v Watford
Plymouth Argyle v Leyton Orient
Birmingham City v Cambridge Untied
Portsmouth v Peterborough United
Millwall v Wycombe Wanderers
Southend United v Walsall
