English champions Manchester City have been drawn to face Southampton away, after the Sky Blues eased past Peterborough 2-0 earlier this week.
Chelsea will make the trip to Middlesbrough, who have already knocked out both Manchester United and Tottenham in their run.
Liverpool will face either of Championship promotion hopefuls Huddersfield Town or Nottingham Forest in the last eight.
The other match puts Crystal Palace up against Everton, who beat Boreham Wood 2-0 on Thursday.
Chelsea were beaten in last season’s final by Leicester City, while Arsenal were winners in 2020.
The games will be played on March 19-20, with no second legs permitted, meaning the winners will be determined after extra-time or shootouts.
FA Cup quarter-final draw:Crystal Palace v EvertonMiddlesbrough v ChelseaNottingham Forest or Huddersfield v LiverpoolSouthampton v Manchester City