"We claim responsibility for sending a booby-trapped parcel to the German finance minister," the Conspiracy of Fire Nuclei group said in a statement posted on an anti-establishment website.
A Greek police source said the claim was "most probably" authentic.
German police on Wednesday said they had discovered the "explosive" package at Finance Minister Wolfgang Schäuble's office building, a day before he was due to host his new US counterpart Steven Mnuchin.
"The package contained an explosive mix," Berlin police said in a statement, adding that the substance is often used in the production of fireworks.
"It was designed to cause severe injuries when the package is opened," they said.
The parcel was intercepted in the ministry mailroom.
Greece's interior ministry said authorities in both countries were working together on the case.
Another Greek police source said the package had a Greek stamp. The "sender" of the parcel was given as Adonis Georgiadis, a deputy leader of the opposition New Democracy party - along with his real address.
Georgiadis, a former far-right politician before he joined New Democracy, said the case was "no joke."
"This is very bad for Greek-German relations," he told Antenna TV, adding that a bookstore he owns in Athens had also been targeted with an incendiary device on Wednesday.
Greek authorities are examining how the package was able to leave the country containing the explosive material.
Schäuble became extremely unpopular in Greece during the country's crippling debt crisis as he was seen as unyielding in imposing austerity on Athens in exchange for financial aid.
Conspiracy of Fire Nuclei, listed as a terrorist organisation by the United States, in 2010 sent letter bombs to foreign embassies in Greece and to three European leaders - then European Commission chairman Jose Manuel Barroso, German Chancellor Angela Merkel and then Italian prime minister Silvio Berlusconi.
One of the letter bombs, which contained gunpowder, ignited and lightly injured a courier company employee in Athens, but most were intercepted by police.
Police in 2011 carried out several arrests and said they had dismantled the group.
Nevertheless, others have kept the outfit's name alive and in October, they claimed responsibility for a bomb that exploded outside the home of a prosecutor.
Nobody was hurt.
"For every comrade in prison, new comrades are ready to replace him," the Conspiracy of Fire statement said.