Christos Markoyiannakis, the deputy public order minister, resigned after calling the judge a "fool" and "illiterate". A sound recording of his recent comments was aired on private television stations.
Greece and Britain have denied allegations that 28 Pakistanis around Greece were kidnapped in July and interrogated by Greek and British agents over several days about the bombings that killed 56 people on three subway trains and a bus.
Greek newspapers have named one British and eight Greek secret service officers allegedly involved. One newspaper also published a photograph of the alleged British officer, a ranking official at the embassy in Athens.
Markoyiannakis' remarks against Supreme Court prosecutor Dimitris Linos came as an embarrassment to Greece's conservative government, hours before the ministers of justice and public order were due to appear in parliament to answer questions on the alleged abductions.
"My private remarks to friendly party colleagues were recorded illegally and an excerpt of this recording was broadcast out of context"
Deputy Public Order Minister,
"I submit my resignation so that I do not place the government in a difficult position," Markoyiannakis, 58, said in a statement.
"My private remarks to friendly party colleagues were recorded illegally and an excerpt of this recording was broadcast out of context."
Last week, three of the Pakistanis who were allegedly abducted said they had been hooded, beaten and subjected to death threats during questioning.
Lawyers representing the 28 immigrants have filed a complaint against the nine agents named by Greek newspapers.
"Months went by and of course the police did nothing to investigate these allegations, neither did the public order ministry," lawyer Frangiskos Ragoussis, who is representing several of the alleged abductees, told private Alpha television Wednesday.
"A judge had to take the file from the police so that the investigation would start in earnest."
On 21 January, Pakistani immigrants and an anti-globalisation group are planning a march in protest against the alleged abductions.