The draw was made earlier today at the UEFA Headquarters in Nyon.
Arsenal Ladies are the most successful club in English women's football having won 40 major trophies to date.
Blues Ladies will have home advantage in the first leg on 22 or 23 March 2014, with the return leg set to played a week later.
Blues Ladies made club history by making it into the quarter-finals of the competition with a 7-2 aggregate win over FK Zoriky, which saw them play at Birmingham City’s St. Andrew’s Stadium for the very first time. While Arsenal Ladies 6-2 aggregate win over Glasgow City.
The semi-final draw was also made today and if Blues can beat the Gunners they will play the winners of the tie SV Neulengbach and Tyresö FF.
Further information on the tweo-legged quarter-final tie will follow in due course.
UEFA Women's Champions League Quarter-Final draw in full:
Tyresö FF v SV Neulengbach
VfL Wolfsburg v FC Barcelona
ASD Torres CF v 1. FFC Turbine Potsdam
Birmingham City v Arsenal
Birmingham City / Arsenal v Tyresö FF / SV Neulengbach
ASD Torres CF / 1. FFC Turbine Potsdam v VfL Wolfsburg / FC Barcelona
Road to Lisbon:
Quarter-finals: 22/23 & 29/30 March
Semi-finals: 19/20 & 26/27 April
Final (Estádio do Restelo, Lisbon): 22 May