After missing out on European football with a seventh-placed finish in the Premier League last season, United entered Wednesday's draw alongside the other 12 top-flight sides not involved in UEFA Champions League or Europa League action this term.
Under the leadership of new manager Louis van Gaal, United will travel to stadiummk in the week commencing August 25 to take on Karl Robinson's men, who finished 10th in the third tier in 2013-14.
Four-time winners of this competition, United reached the semi-finals last season, before being knocked out on penalties by Sunderland.
Gus Poyet's side went on to lose the final 3-1 to Manchester City at Wembley, and will begin their campaign at Birmingham City this time out.
Of the Premier League's three newly promoted sides, Burnley and Leicester City have been handed home ties against Sheffield Wednesday and Shrewsbury Town respectively, while QPR will visit Burton Albion.
West Ham and Sheffield United will face each other for the first time since the Carlos Tevez controversy that surrounded the latter's relegation from the top flight in 2007.
Other ties involving Premier League clubs will see Aston Villa host Leyton Orient, Crystal Palace visit Walsall and West Brom welcome League Two Oxford United.
Newcastle United will make the long trip to Kent to take on Gillingham, while Stoke City face Portsmouth, Swansea City host Rotherham United and Southampton venture to the New Den to take on Millwall.
Draw in full:
Burton Albion v QPR
Port Vale v Cardiff City
Middlesbrough v Preston North End
Stoke City v Portsmouth
Huddersfield Town v Nottingham Forest
Swansea City v Rotherham United
Watford v Doncaster Rovers
Millwall v Southampton
Bournemouth v Northampton Town
Brentford v Fulham
West Brom v Oxford United
Scunthorpe United v Reading
Derby County v Charlton Athletic
West Ham v Sheffield United
Swindon Town v Brighton and Hove Albion
Leicester City v Shrewsbury Town
Crewe Alexandra v Bolton Wanderers
Birmingham City v Sunderland
Gillingham v Newcastle United
Norwich City v Crawley Town
Bradford City v Leeds United
Aston Villa v Leyton Orient
Burnley v Sheffield Wednesday
Walsall v Crystal Palace
MK Dons v Manchester United
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