The Magpies claimed a thrilling 4-3 success over Premier League champions Chelsea at Stamford Bridge in midweek.
Holders United, who beat Scunthorpe in the last round, are at home to Wolves.
Brentford's reward for their penalty shoot-out victory over Everton was a visit to another top-flight team, Birmingham, while Northampton, who stunned Liverpool at Anfield, were handed a trip to Ipswich.
Wigan boss Roberto Martinez welcomes former club Swansea to the DW Stadium.
Northampton boss Ian Sampson told Sky Sports News: "We'll go to Ipswich and hopefully we can reproduce the form we showed at Anfield on Tuesday.
"We've already knocked out a Championship side in Reading and hopefully we can go to Ipswich and do the same thing."
The draw in full for the fourth round of the Carling Cup:
Newcastle v Arsenal; Birmingham v Brentford; Wigan v Swansea; Aston Villa v Burnley; Leicester v West Brom; Manchester United v Wolves; West Ham v Stoke; Ipswich v Northampton.
Ties will be played in the week commencing October 25.