"My heart tells me quite clearly that I cannot stay", Bishop Margot Kaessmann was quoted as saying.
Arrested in Hanover at the weekend, she was charged with passing a red light while three times over the legal limit.
The 51-year-old became Germany's youngest bishop in 1999. She was appointed last year to lead the 25 million-strong Lutheran Church.
"Last Saturday, I made a big mistake," Bishop Kaessmann was quoted as telling reporters on Wednesday.
'Popstar of Protestantism'
"I hereby resign from all my Church responsibilities."
According to prosecutors, Bishop Kaessmann had been "completely unfit to drive" when she was stopped in her Volkswagen Phaeton in Hanover on Saturday.
She faces a fine of a month's salary and a one-year driving ban for the offence.
Bishop Kaessmann, who Spiegel magazine dubbed the "popstar of Protestantism", has a high profile in the Germany.
A divorced mother of four and breast cancer survivor, she made the news recently by calling for the withdrawal of German troops from Afghanistan in a sermon on New Year's Day.
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SIC: BBC