The girl, understood to be a first-year pupil in Wishaw, can be seen squaring up to the boy and punching him repeatedly in the face.
The clip is understood to have been filmed last night and was posted on YouTube.
A spokesman for North Lanarkshire Council said: "The incident happened outwith school hours and away from the school grounds. The incident has been reported to the police who are carrying out investigations.
"Bullying of any kind is not tolerated and our schools have anti-bullying policies and procedures in place."
The two-minute clip shows the girl with her hands in her pockets standing facing the boy who is inches taller.
Someone off-camera can be heard saying: "I need to go home, so if you're going to hit him, hit him."
The girl then says to the boy: "Don't you be cheeky to me, right", pushes him twice and grabs him by the collar.
She can then be seen punching the boy in the face five times.
The boy does not react and attempts to turn and walk away.
The council spokesman said: "A full school investigation will be carried out and action will be taken."
Strathclyde Police said they have been made aware of the footage which has since been removed from the video sharing website.
The force has confirmed that two girls, aged 11 and 15, are now the subject of a report to the Children's Reporter.