The unseeded debutants will host the 2009 runners-up in the Round of 32 at the Academy Stadium on 5/6 October before travelling to Russia on 12/13 October.
A top-two finish in the 2015 FA Super League season clinched the Blues’ first qualification to the competition.
Perm reached the final in their debut season – their best run since reaching the 2011 quarter-finals, in which they lost 1-0 to Lyon.
The Round of 16 will be drawn in late October and played in November. The quarter and semi-finals draws will be conducted in the same month, before the competition then breaks to line up with the men's game, resuming in March for the quarter-finals.
The final will be held at the Cardiff City Stadium on Thursday 1 June 2017.