Eduardo Cunha has been accused of trying to obstruct a corruption investigation against him and intimidating lawmakers.
He is an outspoken critic of President Dilma Rousseff and has led an impeachment drive against her.
Next week, the Senate is due to vote on whether to launch an impeachment trial against Dilma Rousseff.
If a simple majority votes in favor, Dilma Rousseff will be suspended from office for 180 days while Vice-President Michel Temer takes over as interim president.
Under Brazil’s constitution, Eduardo Cunha was the next in line for the presidency after Michel Temer, who is facing impeachment proceedings on charges similar to those facing Dilma Rousseff.
Dilma Rousseff has accused Michel Temer and Eduardo Cunha, who belong to the opposition PMDB party, of being the ringleaders of a “coup attempt” against her.
Eduardo Cunha is suspected of obstructing an investigation into allegations he took $5 million in bribes from companies seeking to secure contracts with state-oil giant Petrobras, which he denies.
Petrobras is at the centre of a massive kickbacks scandal which has led to the arrest of dozens of lawmakers and top businessmen.
Waldir Maranhao, who is also under investigation for his alleged role in the Petrobras corruption scandal, is to become the next Speaker of the House.
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