Mikel Arteta's side failed to qualify for Europe last season – the first time the Gunners have missed out on continental competition since 1996.
It means it will feature in the Carabao Cup second round, with the Premier League's top seven sides given a bye to the third round.
West Brom, which is under the charge of new boss Valerien Ismael, will be its opponent in the week commencing 24 August (AEST).
The last time the sides met, a 3-1 victory for Arsenal at Emirates Stadium in May condemned the Baggies to a return to the second tier.
League Two side Barrow will host Aston Villa, while Southampton and Brentford will also face a fourth-tier team in the form of Newport County and Forest Green Rovers.
Two all-Premier League ties see Burnley travel to Newcastle United and Watford welcome Crystal Palace to Vicarage Road.
EFL Cup second-round draw in full:
Oldham Athletic v Accrington Stanley
Newcastle United v Burnley
Wigan Athletic v Bolton Wanderers
Huddersfield Town v Everton
Sheffield United v Derby County
Stoke City v Doncaster Rovers
Shrewsbury Town v Rochdale
Nottingham Forest v Wolves
Morecambe v Preston North End
Blackpool v Sunderland
Leeds United v Crewe Alexandra
Barrow v Aston Villa
Brentford v Forest Green Rovers
Millwall v Cambridge United
West Bromwich Albion v Arsenal
Norwich City v Bournemouth
Cardiff City v Brighton and Hove Albion
Birmingham City v Fulham
Gillingham v Cheltenham Town
Queens Park Rangers v Oxford United
Swansea City v Plymouth Argyle
Stevenage v Wycombe Wanderers
Newport County v Southampton
Northampton Town v AFC Wimbledon
Watford v Crystal Palace