Several thousand people had gathered in Aotea Square, calling for a ceasefire in Gaza, yesterday.
The child, who was attending the pro-Palestinian rally with his family, was alleged to have been hit in the head twice as the crowds dispersed.
Family friend Mohamed Soliman had been at Starship Hospital, where the boy was taken with serious injuries.
"The family is in shock, of course. Imagine waking up in the morning just like we're going to the protest for our brothers and sisters in Gaza, and then something happens to your own son. Of course that's something that you wouldn't expect, especially in New Zealand," Soliman said.
"Alhamdulillah the child is all good ... he's doing fine now."
Te Whatu Ora Auckland said the child was in a stable condition on Sunday night.
Soliman had been among the crowd chanting in Aotea Square about 5pm, as the march was ending, when people began shouting.
"The police took maybe 30 seconds until they arrived," he said.
He said the child had been hit twice before an onlooker intervened and held a man until police came.
"Then the police took him and pushed him into the wall and then they started moving and taking him to the police car."
The crowd had been shocked, Soliman said, despite having seen aggressive counter-protestors at other events.
Police on Sunday said they had arrested a man after a child was assaulted behind the Auckland Town Hall.
Superintendent Sunny Patel said the man had been receiving mental health services support prior to the attack.
"We understand this incident has been incredibly distressing, and are supporting the victim and their family," Patel said.
"Police are still working to establish the events that occurred in the lead up to this incident and we are speaking with a number of witnesses."
Two other people were also arrested at the protest, but Patel said the demonstrations - which were attended by several thousand people - were mainly peaceful.
Event organiser Rand Hazou said multiple people had voiced concerns about the man to police earlier.
Organisers were "devastated" the group had become the target of "senseless" violence, Hazou said, and said the group's stance was clearly peaceful.
"We try really hard to communicate this message that violence is not the answer, we're anti-violence, and yet we become the target of this kind of senseless violence. It's deeply distressing and deeply upsetting," he said.
