Leaders of both the National Party and Green Party say it was untenable for Kiri Allan to remain as justice minister after her arrest on Sunday night.
Allan was charged with careless use of a motor vehicle and refusing to accompany a police officer, following a car crash in Wellington on Sunday night.
She was also issued an infringement notice for having excess breath alcohol between 250 and 400mcg.
As a result she resigned from all of her portfolios.
National Party leader Christopher Luxon said she made the right decision.
"It was the right thing for Kiri Allan to resign. It was quite untenable for her to continue as justice minister," he said in a statement.
"Clearly this situation raises questions about the judgement of Prime Minister Chris Hipkins.
"We wish Ms Allan well and hope she is getting the support and help she needs."
Hipkins oversaw Allan's return to work after taking some time out to look after her mental health.
Allan had given him assurances she was ready to return to Parliament, he said.
Green Party co-leader James Shaw said Allan's arrest was heartbreaking.
Shaw told Morning Report it was clearly untenable for her to stay on as a minister but he felt sad for her and hoped she was getting the support she needs.
"The prime minister and Kiritapu have made the right call.
"I do think first and foremost that it is frankly heartbreaking, I mean obviously Kiri has been through an incredibly tough time recently and it is possible for people who are in that situation to go for weeks feeling fine and then not being, so I think we just have to acknowledge she's a human being like anybody else and has been going through a very, very tough time."
Ultimately, it was a serious matter, he said.
Shaw did not think it was for anyone to judge whether Allan returned to work too soon.
"You've got to acknowledge, mental health is a big challenge in this country, there are many hundreds of thousands of people who are obviously not in the public eye in the way that a government minister is but who are suffering from the same kind of mental distress challenges and I just hope that they are able to access the support that they need."
Asked if he would agree this was a significant blow to Labour's chances of re-election, Shaw said ultimately in a situation like this, the vast majority of people would see it for what it was - "which is a person who has been in a state of distress and has gone through this episode. I don't think this reflects on the wider Labour team at all".
Ngāti Kahungunu chair Bayden Barber said the iwi will support Allan.
Allan was a talented minister and leader and the iwi will wrap a korowai of aroha around her, Barber said.
In a statement, Allan said after taking time off to address a number of personal difficulties she had believed she "was okay to juggle those challenges with the pressure of being a minister".
"My actions yesterday show I wasn't okay, and I've let myself and my colleagues down.
"I accept that my position as a minister is untenable."