The images show the soldier putting a headlock on the child while women pull on the soldier's back, trying to free the boy.
The altercation took place during a weekly protest Friday organized by Palestinian activists against settlement construction in the village of Nabi Saleh in the West Bank.
The footage was shot by the boy's father, Bassem Tamimi, he told CNN.
The family routinely films its demonstrations, he said, and posts them on a site called Nabi Saleh Solidarity.
The video -- a clip edited from longer footage -- had nearly 3 million views by Sunday.
"This is very difficult for any father or mother to see their son or daughter in that way, being violently attacked," said Tamimi.
In the video, Bassem Tamimi's daughter, A'hed, is seen biting the soldier's right hand in an apparent attempt to free her brother.
A'hed has appeared in previous videos the family has shot and posted online. Two years ago a video was posted that showed her shaking her fist at an Israeli soldier. The soldier reacted by walking away.
Tamimi said he documents all of the protests to keep a record of the conflict there and collect what he says is evidence of Israeli abuses.
Israeli army: Actions were justified
The Israeli army defended its actions, saying that people in the crowd had thrown rocks at the soldiers.
"The forces decided to detain one of the Palestinians identified hurling rocks," an Israeli army spokeswoman told CNN.
The army said the commander at the scene halted the arrest to avoid an escalation of the situation.
Tamimi told CNN that his wife and daughter were trying to free his son and clashed with the soldier, as the video appeared to show.
Some residents of Nabi Saleh have been staging protests for years against Israel's settlement policy.
Sometimes the protests turn violent, with Palestinian youths throwing stones and Israeli soldiers firing tear gas and rubber bullets.