The London Assembly member cited issues over the party’s “mixed messages” on transgender rights as her reason for stepping down.
The move comes just over a week after fellow co-leader Jonathan Bartley announced he would be stepping down, triggering leadership contest in the Autumn.
Ms Berry said in a statement that she would remain in place during the contest, but would not be standing.
In a statement, Ms Berry said: “I have been considering my position as co-leader since the decision was made to announce our new front bench spokespeople.
“And though I will stay on as acting leader through the leadership by-election, I am writing today to say that I have decided not to stand as a candidate in that by-election.”
Mr Bartley and Ms Berry were elected co-leaders of the Green Party in 2018, taking over from the party’s only MP, Caroline Lucas.
The 47-year-old said it had been “incredibly rewarding” working with Mr Bartley and that she was “proud of the progress the party” had made in recent years.
But she added she could “no longer make the claim that the party speaks unequivocally, with one voice” on the issue of “trans rights and inclusion”.
Explaining her decision, the Oxford graduate said the election of new front bench representatives by the membership meant there was “inconsistency” between her own and the party’s stance.
Ms Berry said: “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.
“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.
“Failing to win the confidence of a majority of my colleagues to reflect these is also a failure of leadership. Green leaders do not hold power but we do have a duty to influence, so I must apologise to you all for this failure and hold myself to account.”
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.”