The quotas were supposed to be implemented in May 2026 for the next Senedd elections, but July 2030 was chosen instead.
However, Trefnydd, the head of the house, Jane Hutt, acknowledged in a written statement on Monday night that the plans had been abandoned.
There had been apprehension that the planned measure may face legal opposition.
A number of Senedd lawmakers from different parties stated that they required proof “beyond doubt” that the members possessed the power to approve the bill.
The plans were kept apart from the Senedd’s expansion, which will result in 96 members of parliament instead of 60, a more than 50% increase.
Next week, there will be a debate and vote on a resolution to withdraw the Senedd Cymru (Electoral Candidate Lists) Bill from consideration.
Eluned Morgan, who was appointed first minister of Wales in August, will respond to inquiries from Senedd members later on Tuesday in her first appearance as the new minister.
She traveled throughout Wales during the summer as part of a “listening” exercise, and now she is expected to present her plans for administration.
The administration declared that it will instead look into alternative strategies to ensure gender parity, adding that it was still “committed to a gender-balanced Senedd.”.