Fenton said he had spent time speaking to students this week, in the playground, and they had assured him they felt safe and these fights were anomalies.
In the email to parents, Fenton also called for the video to be taken off social media and said it could breach the Harmful Digital Communications Act.
On Wednesday, a Year 12 Havelock North High girl was knocked to the ground.
She was then stood over by a female Year 11 student and kicked in the head and body, while at least one bystander laughed as the attack was filmed.
The blows include a kick to the victim's head as she lay on the ground.
Another student pulled the attacker away from the victim.
Fenton said he had spoken with a parent of the victim and the parent had ''indicated she was 'fine'.''
Fenton told parents the attackers have been removed from the school and will appear in front of the school board disciplinary committee next week.
"Such was the nature of the attack that the police have also been involved, and are conducting a full investigation,'' Fenton said in an email to parents.
"I met with the police and in addition to the nature of the incident, they are also concerned about the number of people who downloaded the video of the attack, and have shared it with others.
"There is a feeling that this could be a breach of the Harmful Digital Communications Act.
"I would suggest that if your young person has done this and posted the video on social media, that they take it down immediately as it could be an offence."
Fenton said situations like this are unsettling for students.
"I am disappointed that for many students their first reaction is to film and circulate the footage.
"I have no hesitation in saying that staff and students who are new to HNHS frequently comment on how quiet and safe our playground is. That is certainly my opinion of our school.''
After the Napier incident, experts opined that youth violence was increasing during the Covid-19 epidemic.
"Covid-19 has plenty to answer for but these cases in the school are I believe an anomaly,'' Fenton told Hawke's Bay Today.
"We haven't seen anything like this before in my time at the school.''