Green Party co-leader James Shaw's attacker apparently shouted about the United Nations during the incident, Trade Minister David Parker says.
Shaw, 45, was "shaken" after being injured in the violent attack on his way to Parliament this morning, his colleagues said.
Police said a 47-year-old man would appear in Wellington District Court tomorrow charged with injuring with intent to injure.
Green Party co-leader Marama Davidson, speaking alongside colleague Gareth Hughes, 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".
Neither Davidson nor colleague Golriz Ghahraman were aware of any specific comments that might have been directed at Shaw by his attacker.
A spokesman for the party said the man had shouted but it appeared to be random comments.
But a spokesman for Parker said Shaw had told the Minister about the comments made during the attack.
Parker was critical of the role social media played in relaying extreme opinions.
"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 told reporters this afternoon.
"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."
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 this afternoon. He had been grabbed and hit in the face, she said.
• Attacks on MPs over the years
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 spokesman said 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.
The spokesman 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."
He said Shaw did not know the man, and he did not see where he appeared from.
The spokesman said Shaw was very grateful for the people who helped him afterwards and for police and ambulance crews who arrived quickly.
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.
"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.
PM Ardern on Shaw attack
Prime Minister Jacinda Ardern said the attack on Shaw showed New Zealand couldn't take for granted how accessible its politicians were.
"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 afterwards, he told her he was "doing fine".
"I tried to encourage him to take whatever time he needed to recover," she said.
"My thoughts are with James and also [Shaw's wife 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.
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."
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.
Minister for Women and fellow Green MP Julie Anne Genter today delivered New Zealand's National Statement at the 63rd Commission on the Status of Women in New York.
The Green Party has also supported the controversial UN Global Compact on Migration, an international agreement to co-operate on migration issues.
Last month, Damian Collins who chairs the British Parliament's Digital, Culture, Media and Sport Select Committee, said: "democracy is at risk from the malicious and relentless targeting of citizens with disinformation and personalised 'dark adverts' from unidentifiable sources, delivered through the major social media platforms we use every day."