Pavlos Polakis stands accused by Yannis Stournaras, governor of the Central Bank of Greece, of secretly recording a private conversation between the two.
The recording was released on a leftwing website to back up a claim that Stournaras had badgered him over a loan. The governor has charged that Polakis threatened him.
In the other affair, a union leader at Greece's Centre for Disease Control and Prevention has filed a complaint against Polakis accusing him of defamation.
Polakis, who served as deputy health minister in the leftist Syriza government led by Alexis Tsipras, had accused the union leader of corruption amid a scandal over government procurement of vaccines.
It was the first major clash between the incoming conservative New Democracy party government and Syriza, now in opposition, since Greece's July 7 elections.
In separate votes covering the two affairs, 162 and 163 deputies out of the total 300 voted to strip Polakis of the immunity he enjoys as a deputy.
Ahead of the votes, Polakis accused the new conservative government of "political persecution". His fellow Syriza deputies walked out in protest before the votes took place.