The Gunners, looking to win the trophy for a third year on the trot, will back themselves against the Clarets, who currently lie fifth in the English Championship, having been relegated from the Premier League last season.
Elsewhere, reigning EPL champions Chelsea face the winners between MK Dons and Northampton, while an all-Premier league showdown could be on the cards as Manchester City take on the victors in the Aston Villa-Wycombe tie.
The fourth round served up just two more all top-flight ties, a definite being Stoke City’s amtch-up against Crystal palace, while Liverpool – should they advance past Exeter in their replay – have West Ham lying in wait.
All fourth round fixtures will take place between the 29th January and the 1st February 2016.
West Brom or Bristol City vs Peterborough United
Eastleigh or Bolton vs Leeds United
Arsenal vs Burnley
Derby County vs Manchester United
Huddersfield Town or Reading vs Walsall
Exeter City or Liverpool vs West Ham United
Wycombe or Aston Villa vs Manchester City
Shrewsbury vs Sheffield Wednesday
Nottingham Forest vs Watford
Carlisle United or Yeovil vs Everton
Crystal Palace vs Stoke City
Oxford United vs Newport County or Blackburn Rovers
Ipswich Town or Portsmouth vs AFC Bournemouth
Colchester United vs Tottenham or Leicester City
Bury or Bradford vs Hull City
Northampton Town or MK Dons vs Chelsea