Mr Barakzai, a Supreme Court judge, had alleged that foreigners were "interfering" in the panel's work and Afghans had little input in its key decisions. He was one of two Afghans on the five-member UN commission.
A deputy campaign manager for Abdullah Abdullah said the resignation was politically motivated.
"Barakzai's resignation has a direct connection to Karzai. It was Karzai's idea," Saleh Mohammad Registani told the Associated Press news agency.
"Karzai is trying to bring the work of the ECC into question."
'Worthy of praise'
Mr Karzai conceded that some irregularities must have taken place but insisted that the elections were a success.
AFGHAN FRAUD ALLEGATIONS
30 Sep: UN recalls envoy Peter Galbraith following row over the vote recount process
15 Sep: ECC chief says 10% of votes need to be recounted
8 Sep: Poll complaints body orders some recounts nationwide
8 Sep: IEC says votes from 600 polling stations "quarantined"
3 Sep: Claims 30,000 fraudulent votes cast for Karzai in Kandahar
30 Aug: 2,000 fraud allegations are probed; 600 deemed serious
20 Aug: Election day and claims 80,000 ballots were filled out fraudulently for Karzai in Ghazni
18 Aug: Ballot cards sold openly and voter bribes offered
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