James Shaw's attacker is believed to have shouted about the United Nations during the incident, Trade Minister David Parker told reporters.
"I have a personal view that the United Kingdom Government and select committee was recently right to be very critical of extreme opinion feeding political biases and causing instability in some people which is fed through social media platforms," Parker said.
"We need to reflect upon what's going on in society that causes people to be so extreme in their reactions to things they disagree with," Parker said.
Shaw is "shaken" after being injured in the violent attack on his way to Parliament this morning, his colleagues say.
Green Party co-leader Marama Davidson, with colleague Gareth Hughes beside her, said the focus was on supporting Shaw and his family.
"He's shaken, and we are shaken," Davidson told reporters.
Shaw himself told reporters in a text that his black eye "looks worse than it is".
Davidson said there was nothing to indicate at this stage that the attack was because of Shaw's or the Greens' work - though she confirmed the attacker appeared to know who he was.
Shaw remained at hospital for observation. He had been grabbed and hit in the face, she said.
Shaw would not return to Parliament today and was not planning to speak to media.
The Green Party had been overwhelmed by messages of support, Davidson said.
She said it appeared to be a single attack and not a pattern of political attacks.
"We are all upset for our friend but we are all pulling together."
She said the attacker personally identified Shaw, but there was no indication that the attack was linked to the work of the Green Party.
Davidson said she knew nothing about the man arrested in relation to the attack.
She valued the freedom of access to MPs in New Zealand. "I would hate to see that go."
Shaw's press secretary, Peter Stevens, the Greens co-leader was walking past Wellington's Botanic Garden just before 8am when a man started talking to him before grabbing him and punching him several times.
Stevens said Shaw was walking with his headphones on listening to music when the man approached. The attacker seemed to recognise Shaw, he said, but the conversation was brief and somewhat random.
He said Shaw asked the man to let go of him before he was punched.
"He's feeling a bit tender and a bit shaken up," Stevens said.
Stevens said Shaw was very grateful for the people who helped intervene and for police and ambulance crews who arrived quickly.
Meanwhile Prime Minister Jacinda Ardern says the attack on Shaw shows New Zealand can't take for granted how accessible its politicians are.
"I think all of us will probably be united in wanting to ensure we have the kind of political environment where everyone can hold their views, but they can do that safely," Ardern said this afternoon.
Ardern said that when she spoke to Shaw after he was punched, he told her he was "doing fine".
"I tried to encourage him to take whatever time he needed to recover," she said.
Greens co-leader James Shaw suffered a black eye in today's assault. Photo / File
"My thoughts are with James and also Annabel. When you go into politics in New Zealand you just don't expect these things to happen, and I know it will be especially challenging for loved ones.
"I would like to acknowledge the members of the public who quickly came to Minister Shaw's assistance. I understand their quick actions assisted in the arrest.
"We have an environment in New Zealand where politicians are accessible - and that's something we should feel proud of. We are after all, here to serve people. But today's events really show we cannot take that for granted," she said.
Shaw was punched in the face in an apparently unprovoked attack as he walked to work through central Wellington this morning.
Shaw, 45, was walking to the Beehive from his home in Kelburn when he was confronted by a man who stepped out, spoke to him and identified him then hit him in the head, a spokesman for the Green Party told the Herald.
Shaw suffered a black eye in the attack, which happened at 7.50am at the entrance to the Botanical Gardens on Glenmore St, a busy road.
Two passers-by came to Shaw's aid. He was assessed by ambulance staff at the scene before carrying on to the Beehive, just 500 metres away, and attending a Cabinet committee meeting.
Shaw wasn't robbed, and the spokesman said it appeared to be an unprovoked attack.
Shaw then went to Wellington Hospital for an assessment given he received a blow to the head.
Police said they had arrested a 47-year-old man over the attack.
A message from the Official Green Party Twitter page thanked people for their messages of support.
"We're making sure he's resting up and getting checked out. We'll let you know more later today."
The area where Shaw was attacked is a busy commuter thoroughfare and the main route into the CBD from Karori.
There would have been a large number of vehicles travelling on the road, as well as cyclists and pedestrians about.
The Botanic Garden entrance in Glenmore St.
"We understand members of the public have assisted the victim and we believe there may also be other witnesses to the incident," police said in a statement.
The party had sought leave from the House today from the Speaker for Shaw.
As well as being the Greens' co-leader, Shaw is also the Climate Change and Statistics Minister and an associate minister of finance, health and transport.
Green MP Gareth Hughes said in a tweet that the team was shocked by the attack.
"[We] are supporting him today. All Kiwis should be able to walk to work safely."
Also on Twitter, Wellington Mayor Justin Lester said the assault was "outrageous" and "shameful".
"Elected representatives of all hues show courage to represent New Zealanders & we are lucky to have unparalleled access to them. This is a sad day for democracy. Arohanui James," he said on Twitter.
National Leader Simon Bridges said on Twitter that violence was "never okay".
"From myself and The National Party we wish Shaw] a fast recovery. We're thinking of you & look forward to seeing you back at parliament soon."
Ministers don't, as a matter of course, have police protection when they travel. That is reserved for the Prime Minister and ministers who may have received threats.