Figures show an inflation rate of more than 7,500 per cent – the world’s highest.
Lawyers for Ncube, the head of the Catholic church in the Bulawayo diocese, said the photos were an attempt to discredit him.
In a statement the 60-year-old cleric said his decision to resign was aimed at protecting the church from further “attacks” and enable him to challenge the adultery charges privately.
“I remain a Catholic bishop in Zimbabwe and will continue to speak out on the issues that sadly become more acute by the day,” the bishop said in the statement released in Bulawayo, the country’s second-largest city.
The Vatican confirmed that Pope Benedict XVI had accepted the resignation.
Ncube, who had been archbishop since 1998, has been a regular critic of the Mugabe government in Zimbabwe and called for international pressure on the president.
He has accused Mugabe of human rights violations and has called for him to step down.
He has also urged Zimbabweans to demonstrate in the streets against the government as the country experiences rampant inflation and its worst economic crisis since independence.
‘Caught in the act’
But he has kept a lower profile since the pictures allegedly of him appeared in the state-owned Herald newspaper and film footage was broadcast by state media.
The paper said the pictures were taken secretly with cameras set up by a private investigator hired by the husband of the woman involved to secure evidence of the alleged adultery.
The husband is suing Ncube for $160,000.
In August, the Catholic Bishops Conference of Zimbabwe accused the government of making “crude attempts” to divert public attention from the nation’s political and economic crisis by publicising the affair allegations.
The bishops said Ncube had shown courage, moral authority and fearlessness in exposing massacres by government troops in the western Matabeleland province during an armed rebellion after independence in 1980 and a violent countrywide slum clearance operation in 2005.
There was no immediate reaction from Mugabe’s government on the resignation.