She resigns eight days before October 26 repeat presidential election.
In a statement, Dr Akombe said the repeat election as planned can not meet the basic expectations of a credible election.
"I am giving a yellow card to all the political leaders in the country".
The re-run was ordered by the Supreme Court on September 1 after it nullified the August 8 re-election of President Uhuru Kenyatta, following a petition by opposition leader Raila Odinga.
Odinga withdrew from the repeat poll last week, saying the election board had not carried out reforms including the firing of key officials he blames for the mistakes of 8 August.
Chebukati warned that if the current political crisis is not resolved, the country risks finding itself in a situation "possibly worse" than in 2007 and 2008, when more than 1,000 people died in political violence that turned ethnic in nature.
Since the Supreme Court ruling, Kenyatta's main challenger for the presidency, opposition leader Raila Odinga, has pulled out of the rerun, saying that issues around the way the first election was run have not been resolved.
Roselyn Akombe, a senior member of Kenya's electoral commission (IEBC), has fled to the United States amid death threats ahead of next week's presidential election re-run.
Akombe said she had agonized over whether to quit, but had chose to do so because the commission had "become a party to the crisis" and lives were potentially at stake.
"Under such conditions, it's hard to guarantee a free, fair and credible election", he said.
Kenyatta on Wednesday restated his commitment to the poll, but Odinga called for a mass protest on election day - raising the prospect of confrontations between protesters and voters.
Protesters in the opposition stronghold of Kisumu city in western Kenya threw chairs and destroyed tents where an election training camp was being set up for officials.
Akombe had in a statement from NY stated that she had resigned in what she termed as the IEBC's failure to meet the basic expectations of a credible election.
She said that it has become increasingly hard to continue attending plenary meetings where commissioners come ready to vote along partisan lines and not to discuss the merit of issues before them. She told BBC radio she fled after receiving threats from both sides.
The election board said it has conducted some reforms and the vote will go ahead with seven candidates including Odinga on the ballot. In a televised speech on Wednesday, he said: "We walk towards the declared date of the 26th of October both as a God-fearing leadership and government".
President Kenyatta has yet to comment on Ms. Akombe's resignation or Mr. Chebukati's criticisms.