She later joined the Houston Astros organization in 2016 ... eventually holding the same position for their Double-A Corpus Christi affiliate.
Balkovec is a trailblazer in the sport -- she already made history when she was hired as a minor league hitting coach for the Yanks 3 years ago, the first woman to be named to that position.
Balkovec also participated in last season's Futures Game as a coach, becoming the first woman to do so.
The expected promotion has been praised on social media ... with Billie Jean King saying, "History made in baseball! Congratulations to former college softball catcher @_rachelbalkovec on her promotion w/the #Yankees from hitting coach to team manager of the Low A Tampa Tarpons."