Fabiano Silveira was the second minister to exit in the span of a week from Temer's government yesterday, which has only been in power for 18 days following the suspension of Dilma Rousseff for an impeachment trial.
In audio released by Globo television on Sunday night, Silveira was heard talking to Senate President Renan Calheiros and Sergio Machado, the president of Petrobras subsidiary Transpetro, both of whom are being investigated in the embezzlement probe.
The recording was made in March when Silveira was serving on the National Council of Justice.
Brazilian media said Machado recorded the conversation, trading the information for leniency from prosecution.
The presidential palace's media office confirmed Silveira's resignation.
In his resignation letter, excerpts of which were published by Brazilian media, Silveira defended himself and said his remarks were "generic comments and simple opinion, amplified by the climate of political exasperation to which we all bear witness."
Corruption watchdog Transparency International also called for Silveira to step down.
His exit comes about one week after a main Temer ally, Romero Juca, was fired from his planning minister post after another leaked recording in which he apparently said impeaching Rousseff could be a way to derail the Petrobras probe.
The probe, codenamed Operation Car Wash, has seen investigations and prosecutions opened against dozens of politicians and executives -- a who's who of the business and political elite in Brazil -- including Juca.