The revelation that gardai will not be pursuing the matter comes as it emerged that three teens suspended by Christ King Secondary School in Cork are unlikely to face expulsion.
Gardai initially reviewed the incident footage but, as they did not receive a formal complaint, they will not be taking any further action.
The teens are now expected to return to their studies at the school once their suspension is served. But it is expected that they will be handed a stern warning about their future behaviour.
Three girls were suspended by the school on October 12 after an investigation was launched into the shocking video footage, which had been posted online.
The clip showed two teens, both of whom can be identified, punching and grappling on the ground as their violent dispute is filmed by excited onlookers with camera phones.
Around a dozen teens surround the girls as they grappled on the grass.
The fight took place in a park in Douglas, Cork, and the footage shows a large crowd cheering on the combatants.
On several occasions, shouts of "hit her, hit her" can be heard from onlookers.
A number of crowd members are identifiable with both their faces and school uniforms shown. The footage, which was posted on October 10, went viral on the internet and sparked a major debate over teen behaviour and bullying.
Parents groups expressed concern after it emerged dozens of other 'phone fight' clips had been posted on the internet.
The footage indicated that one of the teenage girls appeared reluctant to get involved in the fight, raising bullying fears.
Christ King in Turner's Cross, which identified at least three of its pupils as being involved, said the scenes were "appalling and unacceptable".
"We are disappointed by the apparent presence, and involvement of pupils of Christ King.
"While we cannot control the actions of our pupils outside of school hours, Christ King students represent our school at all times and are advised that the school will invoke disciplinary procedures, as appropriate, where individuals have been found to have brought it into disrepute," a spokesperson said
"Scenes such as those depicted are appalling and unacceptable and may damage the reputation and public perception of Christ King."
Three students were suspended within 24 hours of the school investigation being launched.
No one was hurt in the fight, which lasted around three minutes.