The decision by Justice Teori Zavascki adds to political uncertainty soon before the likely suspension of President Dilma Rousseff from office and the formation of a new government by Vice-President Michel Temer. Zavascki accepted an injunction requested by the country's general prosecutor. Another case against Cunha will be judged later on Thursday by the full Supreme Court.
Cunha, a powerful rival of President Dilma Rousseff, is under investigation for allegedly receiving bribes in the massive corruption scheme at state-run oil producer Petroleo Brasileiro SA.
A spokeswoman for Cunha said he was unaware of Zavascki's decision.
Under Brazil's constitution, Cunha was the third in line to the presidency as lower house speaker.
Rousseff is expected to be suspended from office next week when the Senate votes whether to put her on trial on charges of breaking budgetary laws.