It will be the third time in 10 years the north London rivals have met in the competition, with Arsenal victorious in a two-legged semi-final in 2007, Spurs gaining revenge at the same stage the following year with a 6-2 aggregate scoreline and Arsenal winning 4-1 after extra time in the third round in 2010-11.
The pair were drawn together moments after the hat offered up a second city derby which will pit five-time champions Aston Villa against their local rivals Birmingham.
League Two Carlisle’s reward for upsetting QPR 2-1 was a glamour trip to Anfield to take on Liverpool.
Manchester City will travel to Sunderland, who survived a scare to beat Exeter 6-3, while Manchester United host Ipswich and Chelsea go to Walsall.
There are two more all-Premier League ties as West Ham, entering the competition after their exertions in Europa League qualifying, travel to Leicester and Norwich host West Brom, who needed penalties to get past Port Vale.
Crystal Palace host nearby Championship side Charlton while Newcastle are at home to Sheffield Wednesday.
The remaining Premier League sides remaining in the competition were drawn away from home as Stoke will travel to Fulham, Swansea face Hull, Watford’s conquerors Preston get a visit from Bournemouth and Southampton go to MK Dons.
Everton will travel to Reading if they win at Barnsley on Wednesday night, while Championship sides Middlesbrough and Wolves were drawn together.
The ties will be played during the week commencing September 21.
Third round draw
Middlesbrough v Wolves
Norwich v West Brom
Hull v Swansea
Leicester v West Ham
Aston Villa v Birmingham
Tottenham v Arsenal
Manchester United v Ipswich
Liverpool v Carlisle
Crystal Palace v Charlton
Fulham v Stoke
Sunderland v Manchester City
Newcastle v Sheffield Wednesday
Reading v Barnsley or Everton
Preston v Bournemouth
Walsall v Chelsea
MK Dons v Southampton