Luton - who knocked Wolves out - will travel to Norwich and their fellow Blue Square Bet Premier side Macclesfield have a home tie with Wigan, if the Latics survive their replay at Bournemouth.
Brighton, who upset Newcastle, will host the winners of the replay between Arsenal and Swansea.
Holders Chelsea must travel to Brentford after the Bees overcame League Two Southend in their replay.
Brentford star Sam Saunders said: "It's a great incentive for the lads to get through to the next round. A team like Chelsea, it will be a massive game, a full house and a cracking atmosphere."
Aldershot, the only confirmed League Two side in the draw, will go to Middlesbrough.
Oldham boss Paul Dickov did not get his former club Manchester City as he had hoped, but the Latics - who knocked out Nottingham Forest - still have a mouth-watering home tie against Liverpool.
Luton manager Paul Buckle believes his side have every chance of advancing despite being paired with top-flight opposition.
"It's very exciting for everyone at the club," he told Sky Sports News. "I am delighted for the players as one thing they wanted was a Premier League team.
"I am also pleased it's away from home. It was fantastic to knock out Wolves at home but it will be great for our fans to take in a Premier League atmosphere.
"I know Chris Hughton well and he has already texted me to says he's looking forward to the game, which was really good of him."
Buckle's chairman Nick Owen shares his delight with the draw but admits winning the title is more important to the Hatters.
"It's a terrific draw," he said. "One memory I have of Norwich is that we played them in two epic FA Cup semi-finals in 1959 where we beat them after a replay to get to Wembley.
"It's great for the fans that it is comparatively local as Norwich are only about 90 miles away. It's a tie I am really looking forward to but for me the league has to be our priority for this season."
Draw in full:
Norwich v Luton
Oldham v Liverpool
Wigan or Bournemouth
Derby v Blackburn
Hull v Barnsley
Middlesbrough v Aldershot
Millwall v Aston Villa
Leeds v Tottenham
Brighton v Arsenal
Stoke v Manchester City
Manchester United v Fulham
Brentford v Chelsea
Reading v Sheffield United
Huddersfield v Leicester
QPR v MK Dons
Bolton v Everton
Ties will take place on the 26/27 January