Tottenham travel to the bet365 Stadium to take on Stoke City after getting past Chelsea in a penalty shootout in the previous round.
The final match-up in the draw is Championship side Brentford against Newcastle United.
Carabao Cup quarter-final draw
Stoke City vs Tottenham
Brentford vs Newcastle
Arsenal vs Manchester City
Everton vs Manchester United
The Gunners needed penalties to get past a second-string Liverpool team at Anfield on Thursday night after a 0-0 draw in normal time.
Joe Willock scored the winning spot-kick as Bernd Leno made two big saves in the shootout.
Mikel Arteta fielded a fairly strong XI, including the likes of Leno, Granit Xhaka and £72 million signing Nicolas Pepe.
The German goalkeeper kept Arsenal in the tie in the second half, making a series of key saves as the Gunners progressed to the next round.
Spanish boss Arteta will be looking to claim his second piece of silverware as a manager after guiding his side to FA Cup glory last season.
United breezed through to the quarters with a 3-0 win over Brighton, while Tottenham needed penalties to beat Chelsea, and Manchester City put three goals past Burnley without reply to book their place in the next round.
The quarter-final matches will take place on the week commencing December 21.
The Carabao Cup final will be held at Wembley on February 28, 2021.