In a statement, Petrobras said the company's board of directors was meeting on Friday to study the possibility of naming a temporary replacement.
Another source close to Temer said the president was surprised by the resignation and had not sought to push the CEO out.
The real currency weakened as much as 1 percent against the dollar.
The drop in Petrobras shares wiped some 45 billion reais ($12 billion) from the company's capitalization, according to Reuters' calculations. He sought to align those more closely with worldwide markets through almost daily price adjustments.
But on Sunday Temer, governing with rock-bottom approval ratings, announced plans to placate striking truck drivers - protesting the high cost of diesel - by freezing fuel prices on a monthly basis and taking other measures to bring domestic diesel prices down.More news: Giuliani: Trump team would try to avert subpoena
In this June 1, 2016 file photo, Brazil's President Michel Temer, left, greets Pedro Parente, the then newly named president of state oil company Petrobras, during a swearing-in ceremony, at the Planalto presidential palace in Brasilia, Brazil. "We are going to be, without a doubt, very transparent about this", Parente said.
"Parente's departure means a continuation of the coverage of political interference within the firm", mentioned Gilberto Braga, a finance professor at Ibmec College in Rio de Janeiro.
Shares fell by more than 20% following his resignation on Friday.
Also unresolved is a long-running dispute with the government over an oil-rich offshore area, which could represent a windfall for Petrobras if a deal is reached.
Steep increases in the cost of diesel led Brazil's truckers to block highways across the country starting May 21, disrupting deliveries of basic goods, including food and fuel.More news: Floridians preparing for upcoming hurricane season
The economic and political storm has shaken the lame duck Temer government ahead of October elections and rattled nerves about the path forward for Petrobras, Latin America's biggest oil producer. FUP leader Jose Maria Rangel said by phone that the union "will not be intimidated" by judicial decisions, and called the three-day strike a "warning".
To win over the blockading truckers, who were primarily protesting high fuel prices, the government agreed to lower the average cost of fuel by 46 centavos ($0.12) per liter.
The oil strike was declared illegal by Brazil's top labour court late Tuesday, after Petrobras argued it was about politics rather than labour issues.
"The composition of the rest of the members of the executive board remains the same", the company said.
To pay for the cuts, the government announced it would slash a subsidy for exporters and reduce benefits for beverage makers operating in the Zona Franca low tax zone, which will hit companies such as Coca-Cola Femsa SAB de CV and Ambev SA, a unit of Anheuser Busch InBev NV.More news: England edges ahead of Pakistan on rain-hit day
"For the country, for the company, a great source of uncertainty has opened that is very unsafe", he added.