Allegations of three separate thefts from Auckland and Wellington clothes outlets were aired in the past week by NZ media outlets.
Mr Ghahraman said in a statement released by the party on Tuesday that “stresses relating to my work” led her to act “in ways completely out of character”.
“People should, rightly, expect the highest standards of behaviour from their elected representatives. I fell short. I’m sorry,” she said.
“The best thing for my mental health is to resign as a member of parliament and to focus on my recovery and to find other ways to work for positive change in the world.”
Ms Ghahraman, an Oxford-educated human rights lawyer born in Iran, became NZ’s first refugee MP when elected in 2017.
In recent months, the Auckland-based MP became one of the country’s leading voices for a ceasefire in the Israel-Hamas conflict.
The politically ruinous claims first surfaced on right-leaning website ZB Plus last week.
Ms Ghahraman was stood down from her portfolios after allegations she stole items worth $NZ15,000 ($A14,000) from upmarket Auckland outlet Scotties Boutique.
On Tuesday, CCTV footage of her appearing to steal a handbag was published by the NZ Herald.
The 42-year-old MP was overseas on a private trip until Monday, when senior Greens including co-leaders James Shaw and Marama Davidson met in Auckland to discuss her future.
Mr Shaw said he had a “a lot of empathy for Ms Ghahraman, who was “clearly in a state of extreme distress”.
“She has taken responsibility and apologised. We support the decision,” he said, detailing alarming threats she encountered during her six years as an MP.
“Golriz herself has been subject to pretty much continuous threats of sexual violence, physical violence, death threats, since the day she was elected,” he said.
“There have been police investigations into those threats almost the entire time … if you’re living with that level of threat in what is already quite a stressful situation there are going to be consequences.”
The Greens were made aware of the allegation on December 27, but did not share it publicly.
Police are continuing investigations into the alleged thefts.
Ms Ghahraman will be replaced in parliament by another Greens candidate, Celia Wade-Brown, a former Wellington mayor.
Should she not have resigned, Ms Ghahraman may have been forced from parliament.
Under NZ electoral law, any MP who is found guilty of a crime which could draw an imprisonment term of at least two years is disqualified from parliament.
The maximum penalty for theft of an item worth more than $NZ1000 ($A930) is seven years’ prison, meaning a conviction would have seen Ms Ghahraman ejected.
In the six days between the publication of allegations and Ms Ghahraman’s exit, one of the parties in NZ’s right-leaning coalition government appeared to make merry at her expense.
“We’re ensuring real consequences for low level offences like shoplifting,” a NZ First social media post read, a reference to one of their campaign promises.