The holders booked a place in the Sixth Round with a hard-fought 1-0 win away at Sheffield Wednesday.
Newcastle, who sit 14th in the Premier League, beat West Brom 3-2 on Tuesday night to earn their place in the next round.
The game will be played on the weekend of Saturday 21 March, with winning clubs collecting £720,000 from the FA’s prize fund.
Full FA Cup quarter-final draw:
Sheffield United v Arsenal
Newcastle United v CITY
Norwich v Manchester United
Leicester v Chelsea