Shares of the company, commonly called Petrobras, were down more than 20 percent in midday trading on Friday following the resignation. Shares in Sao Paulo were suspended after Parente's resignation.
In a statement, the company said the board will choose an interim CEO on Friday and that the company's other top executives will remain.
In his resignation letter, Parente said that he "delivered what he promised" when he took over Petrobras two years ago.
However, Parente said his presence in the company is no longer positive in light of the trucker strike, which ground the nation's economy to a halt.
Petrobras unveiled a plan last June to review fuel prices more frequently. For nearly a year, the company has been allowing prices to fluctuate with international benchmark crude futures.
Fuel prices have surged in Brazil as oil futures hit 3½-year highs above $80 a barrel, stoking a wave of discontent across the country. Parente said the strikes had put "the Petrobras price policy under intense questioning."
Since taking the helm of Petrobras in May 2016, Parente has been at the fore of an effort to turn around the Brazilian energy giant. Petrobras became the world's most indebted oil company amid a corruption scandal that gripped the country and led to the imprisonment of former President Luiz Inacio Lula da Silva.
Under Parente, the company has begun to chip away at its massive debt load, which stood at 270.71 billion reais, or $76.23 billion, in the first quarter of 2018, Reuters reported. The company posted its biggest quarterly profit in five years during the quarter, according to the news agency.
Parente put an emphasis on exploiting crude oil production off the coast of Brazil located under thousands of feet of salt. Last November, he told CNBC that the high productivity and low cost of extracting this so-called pre-salt production would be a critical to keeping Petrobras competitive.