"It's not enough to just inform. We need an open debate in plenary assembly," Göring-Eckhardt said in an interview with the Süddeutsche newspaper published on Thursday.
"A statement from the Chancellor is the least we should expect from the federal government."
On Wednesday, Foreign Minister and leader of the centre-left Social Democrats (SPD) Frank-Walter Steinmeier and Defense Minister Ursula von der Leyen, from the rulling Christian Democrats (CDU), announced that Germany was making preparations to deliver arms to the embattled Peschmerga forces in the Kurdish province in Northern Iraq.
Göring-Eckhardt criticised the way the decision was simply made without debate from all sitting parties. "This is a paradigm shift."
Germany, still uncomfortable with its role as instigators of the two World Wars, stays away from foreign military engagements and, as a rule, does not export weapons to active conflict zones. The SPD is also against it in principle. However, Steinmeier had already signalled that rules were meant to be bent, and sometimes even broken.
"The brutality of the terrorist militia Islamic Stat (Isis) could make it necessary," he told journalists on August 14. "The principles must also take into account that there are exceptional circumstances where a political decision in the interest of political security."
Eckhardt-Göring expects to combine with the socialist Left party, also in opposition in the Bundestag, to force a special meeting of Parliament in the next week.
"It is still unclear what weapons will be delivered and under which conditions. A decision like that should not be made behind closed doors," she said. "The people have the right to an explanation."
The Green party leader also called for more humanitarian aid and for Germany to take on more refugees.