The fixture will be played in the week commencing 11 August 2014, with the actual date and kick-off time confirmed once television selections have been made.
League Two side Cambridge United are managed by Richard Money, who guided the U's back to the Football League with a 2-1 win over Gateshead in the Conference play-off final in 2014.
The last time that Blues and Cambridge United met in a competitive fixture was a League Division Two match in April 1995, which the U's won 1-0.
In total, there have been eight league matches between the sides, with Blues winning three of them, Cambridge four and one ending in draw.
The full Capital One Cup first round draw is as follows:
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
All ties to be played week commencing 11 August 2014.