The tie will take place during the weekend of March 19-21.
Last time they met was on January 1, 2020, when City inflicted the first defeat of Carlo Ancelotti’s Everton tenure with a 2-1 win at the Etihad Stadium.
The two sides meet next Wednesday at Goodison Park in the Premier League, with City looking for a fourth consecutive win at Goodison.
Pep Guardiola’s side are currently top of the Premier League, having won their last 15 matches in all competitions.
While Everton beat Rotherham United, Sheffield Wednesday and Tottenham Hotspur to make it to this stage, City saw off Birmingham City, Cheltenham Town and Swansea City to reach the quarter-finals.
Everton have won the competition five times in their 142-year history, but their FA Cup triumph over Manchester United in 1995 remains their most recent piece of silverware.
This year’s FA Cup run is already their longest since 2016, when they were knocked out in the semi-finals by United under Roberto Martinez.
City have six FA Cups in their trophy cabinet, most recently in 2019, when they thrashed Watford 6-0 in the final.
Everton’s Premier League game scheduled for the weekend of March 19-21, away to Sam Allardyce’s West Bromwich Albion, will be rearranged in due course.
FA Cup: Full Quarter-Final Draw:
Everton vs Man City
Bournemouth vs Southampton
Leicester City vs Man Utd
Barnsley or Chelsea vs Sheffield United
Ties to be played during weekend of March 19-21