The video, filmed on a mobile phone and posted on the internet appears to show the girl attempting to provoke a bigger boy.
Eventually she appears to push the boy before punching him five times. She tries to provoke him again and the boy can be heard saying: "I don't hit lassies."
She punches him once more before the video ends.
The Strathclyde Police Facebook page was flooded with complaints, with people demanding officers investigate the incident, understood to have happened on Tuesday in Wishaw, North Lanarkshire.
A second girl filmed the incident and urged the attacker to hurry up and hit the boy, as she wanted to get home.
It is thought all three people involved are pupils at a local secondary school.
A spokeswoman for Strathclyde Police said: "Inquiries are ongoing."
The video has been viewed by thousands of people. Furious Facebook and Twitter users reacted with disgust and the attacker, thought to be 12, has been named on social media sites.
However, the Scottish anti-bullying service respectme has warned that demonising the attacker is not helpful.
Pamela Graham from respectme said: "While the girl involved needs to be held accountable for her actions, there's a risk that, as these videos go viral, those involved get demonised.
"Responses of this kind aren't helpful – it's the behaviour that needs to be challenged and addressed."
A spokesman for North Lanarkshire Council's Learning and Leisure Services said: "We can confirm that an incident involving two pupils from one of our schools took place last night.
"A full investigation will be carried out."