The Blues will travel to the Stoke Gifford Stadium on Sunday 26 March.
The pair meet for the fourth time, with each having registered two victories.
Their last meeting arrived in September 2015, with City running out 6-1 winners in the Super League.
City have never won the FA Cup, having been defeated by Chelsea in all three seasons.
Bristol have reached the final twice in the past six competitions.
Quarter final draw:@BCLFC v @ArsenalLadies @ChelseaLFC v @SAFCLadies @bristolcitywfc v @ManCityWomen @LFCladies v @Official_NCLFC
— SSE Women’s FA Cup (@WomensFACup) March 20, 2017
FA Cup final
The Final will take place at Wembley Stadium and tickets are on sale.
All children can attend for free, while adult tickets are priced £15. The price of an adult ticket drops to just £7.50 when booked as a group of nine or more.
Tickets can be purchased via TheFA.com/Tickets or by calling 0844 826 2010.
