No current Green MPs have put their names forward, including high-profile Auckland Central MP Chlöe Swarbrick who had been the focus of much speculation but on Monday ruled herself out.
As of Monday, Kerekere had left the door open to running against Shaw, saying she was "considering options" and would release a statement after this morning's caucus meeting.
In a statement prior to caucus, Kerekere confirmed she would not be running.
"The whole Green caucus was surprised by the decision of our AGM to reopen nominations for the co-leader role," Kerekere said.
"Like many of my fellow MPs, I received many messages following the AGM; asking me to stand and some members asking me to support other candidates.
"I have taken the time to reflect and discuss with my whānau, party members and caucus colleagues once we were all in a clearer head space before making any decisions regarding the outcome of recent events.
"Having done so, I will not be running for co-leader of the Green Party of Aotearoa New Zealand in this election."
Kerekere said the vote against Shaw showed the need to listen to members and provide more accountability from co-leaders.
"I believe this election presents an opportunity for any and all candidates who may run to clearly state the progressive, left-wing values which are the only way to achieve the critical system shifts we need to uphold Te Tiriti o Waitangi, address climate change and inequality, and protect biodiversity.
"As we head into the local body elections and the next general election, it is critical for me to continue to push from within and keep our co-leaders and MPs accountable to all we say and do."
The official nomination process is to open soon and from which point candidates will have a week to come forward.
If there are multiple candidates, a vote among party members will take place within four weeks.
If Shaw remains the sole candidate, the same process as occurred on Saturday will take place, with the options to re-affirm him as co-leader or open it up again to challengers.
On Monday, Shaw said events of the weekend showed how much members cared, and if successful he would "redouble efforts" over the environment and poverty.
It was clear there was a lot more work to do and he remained frustrated they had not gone as fast as they should, Shaw said.
Government could be "glacially slow" and did not match the speed of the climate crisis.
Over the coming weeks and months Shaw said he would listen to members up and down the country.
Prime Minister Jacinda Ardern has confirmed even if Shaw were to lose his position in the Greens he would retain his ministerial portfolio.
Ardern said her decision to put him in that portfolio was not because they needed a relationship strictly with the Greens but that Shaw was the "right person for the job".
He had helped the Government make the "most significant" progress in climate action than any other government.
Party delegate Trav Mischewski, one of the 32 Green delegates who voted against Shaw's re-election, told the Herald it was to start a "conversation" about leadership rather than simply a vote of no confidence in Shaw.
"Let's have a conversation about where our party's going, what that's going to look like.
"There's been a growing dissatisfaction with where we are, that we're stagnating, hitting the centre with James' steering wheel.
"Even if James is to retain his position, then he's been challenged and he'll have at least engaged more effectively with the membership."
