The announcement comes after Pope Francis last week passed a landmark new measure to oblige those who know about sex abuse in the Catholic Church to report it to their superiors, in a move which could bring countless new cases to light.
Vilson Dias de Oliveira, 60, confessed to Brazilian police in April that he had swiped $4,000 from parish funds for personal use, telling them he did so because he was having financial difficulties, local media said.
Dias also allegedly protected a priest accused of sexual abuse.
The Vatican always announces when Pope Francis has accepted the resignation of a bishop, but never explains why.
Dias also admitted to investigators that he had bought two coastal properties in Brazil worth more than one million reais ($250,000), but claimed he had used his family’s money and his income from the church, news portal G1 said.
“Dear brothers and sisters, in recent months we have had to bear all sorts of crosses through attacks against our… church, against me and other presbyters,” Dias said in a statement.
He added that while he acknowledged his “limitations,” he carried the love of supporters in his heart.
“I ask to resign for the love of Christ and for the good of the diocese,” he said in the letter published by the diocese of Limeira, a city in the Sao Paulo state in southern Brazil.
Dias has been temporarily replaced by Orlando Brandes, the Archbishop of Aparecida.
Brandes told reporters that if Dias were convicted he would “leave the ministry by order of Rome.”
“He will still be a priest, of course, but a priest that is disconnected from the Church,” he added.
It was a “sanitary measure taken urgently by the Pope,” said Fernando Altemeyer Junior, a professor of theology at the Catholic university PUC Sao Paulo.
“The diocese is in pieces,” Altemeyer said.
“The bishop appointed on a temporary basis will play a transitional role and try to heal the wounds.”
The Catholic Church has been rocked by a global pedophilia scandal, with victims coming forward in countries ranging from Australia to Chile, Germany and the United States.
‘Not just him’
News of Dias resigning was greeted with a certain fatalism by Catholic faithful outside the Sao Paulo Cathedral.
“It’s not just him,” Odila Lisboa, 84, told AFP. “How many serious problems do they have over there in the Vatican?”
Clodomiro Campos said Dias should be dismissed if the allegations were proven.
“There are things that shouldn’t happen — what’s right is right and what’s wrong is wrong,” the 60-year-old man said.
While sex abuse scandals have been exposed in other Latin American countries, most recently Chile, the issue has been “invisible” in Brazil for years, said Anne Barrett Doyle, co-director of advocacy group bishopaccountability.org.
“It’s just odd and striking given the enormity of the Catholic population in Brazil and the fact that the crisis has been exploding in other Latin American countries,” Doyle told AFP.
“There have been no government or prosecutorial inquiries into the Catholic church or litigation (in Brazil).”
While Brazil remains the world’s biggest Catholic country, its flock has shrunk while Evangelical churches grow.
Around 64 percent of the population identified as Catholics, according to the 2010 census. That compares with 74 percent in 2000 and more than 90 percent in 1970.