"Media were informally briefed that the mother of the suspect is a member of the Red Army Faction," the police said in a statement, referring to the violent German leftwing Baader-Meinhof group.
"This has nothing to do with the case," the statement added.
Citizens Protection Minister Christos Papoutsis called on police to halt the release of information before the close of operations, it added.
German federal prosecutors had earlier denied the claim that the 27-year-old German arrested in Athens last week, Marie Fee Meyer, is the daughter of Barbara Meyer, wanted for years by German police.
"From what we know at the moment, the young woman who was arrested is not the daughter of former RAF terrorist Barbara Meyer," a spokesman for the German federal prosecutor's office told AFP over the weekend.
The German foreign ministry on Monday confirmed a German national had been arrested in Athens but refused to give further detail.
Marie Fee Meyer was taken to a prosecutor on Monday along with four other Greek suspected militants who police said had planned attacks ahead of a trial of suspected anarchist bombers that opened in Athens earlier in the day.
The five were caught in Athens on Friday and charged with membership in an extremist organisation and illegal arms possession.
During a raid of their apartment following their arrest, authorities discovered a "draft plan" to attack justice officials, a police press release said Saturday.
Police said they found a "list of magistrates, addresses of police stations, with plans and photographs of weapons" during the raid on the apartment and also seized an AK-47 assault rifle, a pistol and ammunition.
The German woman has denied involvement with the group and requested a lawyer, who said that she was only friends with one of the suspects.