Manchester City were first out of the bag with an away tie with West Brom.
Chelsea will host Nottingham Forest while Liverpool are away to Leicester.
Arsenal will face Doncaster Rovers at the Emirates and Everton take on Sunderland.
A total of seven Premier League clubs entered the competition at this stage, including last year's winners United.
Jose Mourinho's side saw off Southampton at Wembley in February to complete the first part of a double that included the Europa League.
Carabao Cup Third Round Draw in full
West Brom v Manchester City
Everton v Sunderland
Leicester City v Liverpool
Manchester United v Burton Albion
Brentford v Norwich City
Wolves v Bristol Rovers
Burnley v Leeds United
Arsenal v Doncaster Rovers
Bristol City v Stoke City
Reading v Swansea
Aston Villa v Middlesbrough
Cheslea v Nottingham Forest
West Ham United v Bolton Wanderers
Crystal Palace v Huddersfield Town
Tottenham Hotspur v Barnsley or Derby County
AFC Bournemouth v Brighton & Hove Albion