SÃO PAULO—Brazilian investment bank BTG Pactual SA, whose co-founder and now former chief executive has been ensnared in the nation’s largest-ever corruption probe, is moving quickly to restructure as it scrambles to survive the blow to its reputation.

André Esteves, who resigned as chairman and CEO on Sunday, has given up his controlling shares, the bank said Wednesday. Just hours earlier, BTG announced the sale of a stake in local hospital operator Rede D’Or São Luiz for 2.38 billion reais ($616.9 million) to Singapore’s sovereign-wealth fund GIC Pte. Ltd.

Authorities jailed Mr. Esteves last week on allegations of witness tampering and obstruction of justice. Prosecutors allege Mr. Esteves tried to buy the silence of a key witness whose testimony could potentially implicate the banker in a massive graft scandal at state-controlled oil company Petróleo Brasileiro SA.

Mr. Esteves’s lawyer said last week that Mr. Esteves denied the allegations and would fight to clear his name. His lawyer couldn’t be reached on Wednesday for further comment.

The billionaire deal maker swapped all his voting shares in the bank for preferred shares with no voting rights, and didn’t receive any cash, a person close to the bank said Wednesday. Mr. Esteves owned 28.8% of BTG Group, which controls BTG Pactual, before the transaction.

The exchange left BTG under the control of its other top seven partners, who have agreed that management decisions will require the approval of at least four of the partners, the same person said.

The bank will need to do more, both to convince investors and depositors that Mr. Esteves no longer influences bank decisions and to make sure the bank remains solvent after a wave of withdrawals that followed his arrest, said Joao Augusto Frota Salles, an analyst at consultancy firm Lopes Filho Consultoria based in Rio de Janeiro.

“Esteves’s giving up control isn’t enough,” he said. “It will be hard for depositors to believe that the other directors didn’t know” about any illegal activities.

Separately, Brazilian investigators said Monday they have uncovered evidence that BTG Pactual paid a powerful lawmaker 45 million reais in exchange for political favors. The bank has denied wrongdoing.

The price of BTG’s traded units has plunged more than 30% in recent days, and on Tuesday the bank lost its investment-grade status from Moody’s Investors Service. The ratings company downgraded BTG’s rating by two notches to Ba2 from Baa3 and kept it under review for a potential further downgrade.

The sale of the stake in Rede D’Or, which operates close to 30 hospitals in four Brazilian states, is probably just the first of several divestitures, analysts said. Rede D’Or is controlled by the Moll family, which had more than 60% in the company. In April, private-equity firm Carlyle Group LP said it was investing 1.75 billion Brazilian reais for an 8.3% stake in Rede D’Or.

“The question of the bank’s solvency is still a big problem, until they sell more assets,” said Max Felipe Bohm, an analyst at Empiricus, an independent research company based in São Paulo, who added that he expects more sales in coming days. “We need to know how BTG is going to deal with the need to honor its commitments.”

BTG said this week that it is ready to sell more assets, mainly loan portfolios, in order to increase its liquidity. Pactual ended the third quarter with a total loan portfolio of 98 billion reais.

The bank’s possible liquidity issues and the allegation that it bribed a congressman make it difficult to make forecasts about the bank’s future, analysts say.

Markets are still waiting to learn what, if anything, the bank’s top management apart from Mr. Esteves knew about the alleged payments to the congressman, said Luis Santacreu, an analyst at Austin Ratings in Sao Paulo.

“We don’t know how much he, as chairman, got the bank involved too,” Mr. Santacreu said. “But the bank is making the effort to stop the situation from getting worse.”