Speaker Keria Ibrahim is also a top official in Tigray People's Liberation Front (TPLF), one of the country's major political parties that have opposed the postponement.
The parliamentary and regional elections had been planned for August, ahead of the end of incumbent Prime Minister Abiy Ahmed's term in September. No new date has yet been set.
In a televised speech, Keria accused Abiy's government of taking away Ethiopians' sovereign rights, without elaborating.
She was widely understood to refer to the government's decision to postpone the elections, which effectively allowed Abiy to continue ruling beyond the expiry of his term.
"I can't be an accomplice when the constitution is being violated, and a dictatorial government is being formed," she said. "I have resigned not to be collaborator [with] such a historical mistake."