Both Spurs and the Gunners won their respective fourth-round ties on Wednesday.
And they have now been drawn together in the fifth round of the competition.
"I think it's an exciting game. Another derby. I always like to face big teams. It's very good to face Unai Emery and all his staff," Tottenham manager Mauricio Pochettino told Sky Sports following the draw.
"We are very good friends from Spain. A great manager and great coaching staff. It's a massive challenge and I am so excited to play him. Added to that it's a derby, so it will be fantastic."
Elsewhere, Chelsea and Bournemouth will make up another all-Premier League tie, with the Blues barely escaping against Frank Lampard and Derby County on Wednesday.
League One side Burton Albion and Championship side Middlesbrough are the only two non-Premier League teams remaining in the competition, and they will face off in another quarter-final.
Leicester City were set to face Southampton on Tuesday, but the match was postponed following the tragic death of Foxes chairman Vichai Srivaddhanaprabha in a helicopter crash.
The Carabao Cup quarter-final matches will be played during the week commencing December 17.
Full Carabao Cup quarter-final draw:
Arsenal vs Tottenham
Leicester/Southampton vs Man City/Fulham
Middlesbrough vs Burton Albion
Chelsea vs Bournemouth