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The reduction in retail outlets will save the company 750 million reais, with savings mounting to 3.8 billion reais ($1.12 billion) if the full amount of voluntary redundancies takes place.
A minimum 9,300 of the total 109,159 jobs are scheduled for cutting, the bank said in a statement. Severance packages will include 12 to 15 months' salary.
Reductions of working days from eight to six hours are also being offered as a cost-cutting measure.
Sao Paulo's stock market responded positively, with Bank of Brazil shares rising 4.45 percent on the news.
Brazil is struggling through its worst recession in decades although the economy is set to bottom out in 2017 and return to slight growth.