The move comes just over a week after co-leader Jonathan Bartley announced he would be stepping down at the end of July, triggering an autumn leadership contest.
Ms Berry said on social media that she would remain in place during the leadership contest but would not be a candidate.
In a statement, the London Assembly member said she faced an "inconsistency" between her "sincere promise to fight for trans rights" and "the party's choice of frontbench representatives."
Ms Berry does not name any individuals but last month the Greens selected Shahrar Ali, the party’s former deputy leader, as the spokesperson for policing and domestic safety.
In her statement, Ms Berry wrote: "I must stand by our policies and my pledges made to Londoners in the recent election, and there is now an inconsistency between the sincere promise to fight for trans rights and inclusion in my work and the message sent by the party’s choice of front bench representatives."
She continued: "This inconsistency has left me in a very difficult position. I can no longer make the claim that the party speaks unequivocally, with one voice, on this issue."
"And my conscience simply cannot agree with the argument that there is anything positive in sending these mixed messages, especially when the inclusive attitudes of our membership and wider society are clear."
The London Assembly member continued: "Failing to win the confidence of a majority of my colleagues to reflect these is also a failure of leadership."
She called for members to consider whether the Greens would "continue to embrace the principles of listening and solidarity when minority groups are singled out for attack" when electing a new leadership team.