This will be the first ever meeting between City and Tomiris-Turan, who were beaten to the Kazakhstan Women's Championship title by BIIK-Shymkent.
The Champions League debutants are based in the city of Turkistan in southern Kazakhstan.
Should Gareth Taylor's side prevail in that fixture, they will face one of Real Madrid or SK Sturm Graz in the Round One final, after all four teams were drawn in Group Four of the league path.
City have recent history with Real Madrid, having lost a nervy two-legged tie against the Spanish giants at the Round Two stage of last year's competition.
These matches will be played in a mini-tournament style. The semi-finals will be played on Thursday 18 August and the final will follow on Sunday 21 August.
All of these matches will be played at the same location. That venue and details of the kick-off times will be confirmed in due course.
The winners of this mini-tournament would then need to get through a two-legged Round Two tie in order to qualify for the 16-team group stage that begins in October.
The Round Two draw will be made on 1 September before the fixtures are played later that month.
This is the second season of the new format and City's seventh consecutive season in the UEFA Women's Champions League.
Gareth Taylor's team qualified for this year's competition following a third-placed finish in the Barclays Women's Super League in 2021/22.