The matches will be played across the weekend of 21 and 22 March.
Pep Guardiola’s City side progressed to the last eight with a 1-0 win at Championship side Sheffield Wednesday to continue their quest for a domestic and European cup treble.
Six-time winners Newcastle made the quarter-finals for the first time since 2006 with a 3-2 win at Championship leaders West Brom.
Arsenal had become the first team in the hat when they beat League One Portsmouth on Monday, while Sheffield United progressed to the quarter-finals for the first time since 2014 with a 2-1 extra-time win at Reading.
Chelsea beat runaway Premier League leaders Liverpool 2-0 on Tuesday thanks to goals from Willian and Ross Barkley while Leicester edged out Championship side Birmingham 1-0 thanks to right-back Ricardo Pereira’s late header.
Norwich reached the quarter-finals for the first time since the 1991-92 season by beating Tottenham 3-2 on penalties after a 1-1 draw.
FA Cup quarter-final draw
- Sheffield United v Arsenal – Buy FA Cup Tickets
- Newcastle v Manchester City – Buy FA Cup Tickets
- Norwich v Manchester United – Buy FA Cup Tickets
- Leicester City v Chelsea – Buy FA Cup Tickets