Allegations of three separate thefts from Auckland and Wellington clothes shops had been aired in the past week by NZ media outlets.
Mr Ghahraman said in a party statement on Tuesday that "stresses relating to my work" had led her to act "in ways completely out of character".Â
"I am not trying to excuse my actions, but I do want to explain them," she said.
"People should, rightly, expect the highest standards of behaviour from their elected representatives. I fell short. I'm sorry.
"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 she was 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 allegations surfaced first on right-leaning website ZB Plus last week.
Ms Ghahraman was accused of stealing from upmarket Auckland outlet Scottie's Boutique on December 23, and subsequently stood down from her portfolios.
A second allegation of theft from the same outlet was then published, with ZB Plus alleging clothes worth $NZ15,000 ($A13,969) were stolen.
The Auckland-based MP, overseas on a private trip until Monday, stayed silent until Tuesday.
The Greens were made aware of the allegation on December 27, but kept it to themselves.
Greens leaders Marama Davidson and James Shaw said they wanted to wait for Ms Ghahraman to return to discuss the matter, and Scottie's Boutique management also wanted it dealt with privately.
On Tuesday, the co-leaders said Ms Ghahraman was clearly "in a state of extreme distress".
"She has taken responsibility and apologised. We support the decision she has made to resign," they said.
"Golriz Ghahraman has been the leading voice in parliament for human rights, truly independent foreign policy, and electoral reform for six years. Her political achievements are significant."
Police are continuing investigations into the allegations.
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.
While Ms Ghahraman may not have received such a hefty punishment, given the maximum penalty for theft of an item worth more than $NZ1000 ($A930) is seven years' prison, a conviction would have seen her ejected.
In the six days between the publication of allegations and Ms Ghahraman's exit, one of the parties in NZ's right-leaning coaltion 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.
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