The sweeping corruption scandal shaking Brazil’s establishment intensified on Tuesday after the police arrested the mastermind of the military’s secret nuclear program during the 1970s and ’80s.

With the arrest of that figure, Othon Luiz Pinheiro da Silva, a retired navy admiral, what started as a bribery inquiry at the national oil company, Petrobras, seems to have taken on a life of its own, with one prominent figure after another becoming ensnared in accusations of a broad web of graft involving state-controlled enterprises and some of the country’s most powerful private companies.

Prosecutors said Mr. Pinheiro da Silva, 76, took more than $1.3 million in bribes as chief executive of Eletronuclear, a public company that operates two nuclear power plants. The bribes, which the prosecutors said were paid from 2009 to 2014, were related to contracts with construction companies building a third plant, Angra 3, near Rio de Janeiro.

During the military dictatorship, which lasted from 1964 to 1985, Mr. Pinheiro da Silva, a nuclear engineer educated at the Massachusetts Institute of Technology, oversaw a clandestine operation to build reactors for submarines.

“Corruption in Brazil is endemic and is in the process of metastasis,” Athayde Ribeiro Costa, a public prosecutor, told reporters.

If the charges are true, the pattern of graft at Petrobras seems to have been replicated in parts of Eletrobras, the giant public electricity company that controls Eletronuclear. The leadership of Eletronuclear had already come under criticism after costs ballooned for its new nuclear plant, doubling to about $4.5 billion.

Mr. Pinheiro da Silva, a nationalist fixture in Brazil’s military hierarchy, was named chief executive of Eletronuclear in 2005, during the administration of Luiz Inácio Lula da Silva, the mentor and predecessor of President Dilma Rousseff.

Mr. Pinheiro da Silva, a vocal defender of developing Brazil’s nuclear capabilities, had been on leave since April from Eletronuclear, after he was identified as a recipient of bribes by a construction company executive who reached a plea deal with investigators.

A lawyer for Mr. Pinheiro da Silva did not immediately respond to requests for comment.

The scandal has kept Ms. Rousseff on the defensive, with some critics even calling for her impeachment. No testimony has emerged indicating that the president personally profited from the bribery scheme, but her opponents point out that she closely oversaw the expansion of public energy companies in the previous decade as energy minister and later served as Mr. da Silva’s chief of staff before mounting her own presidential campaign in 2010.

This month, federal prosecutors said they had opened an investigation into possible influence peddling by Mr. da Silva himself.

The scandal has sent shock waves through the executive suites of some of Brazil’s largest companies. Over the weekend, the authorities transferred eight executives accused of allowing the bribery scheme to flourish to a prison complex in southern Paraná State after a police holding facility became too crowded because of the rising number of arrests.

The jailed men include Marcelo Odebrecht, the billionaire chief executive of Odebrecht, the construction giant that ranks among Brazil’s largest employers.