Far-right activist Neil Erikson posted a video of the incident on social media.
In the video, Mr Erikson and his group film the individuals playing football, despite being asked "can you stop that" three times.
"It's a public area mate, we can film where we want," one of Mr Erikson's group says, persisting with the filming.
As the situation begins to escalate, police move in.
"I'm not escalating ... It's a public area, I'm legally allowed to film," one of Mr Erikson's group tells police.
An altercation ensues and police pull a man of African heritage to the ground.
One of Mr Erikson's group can be heard saying, "yes, yes, yes".
A 25-year-old was arrested for allegedly assaulting an officer.
On Saturday, Ms Neville said, "people will continue to see a large number of police across our beaches" over summer.
"I would encourage all people not to attempt to incite violence and cause trouble on our beaches or streets," she said.
It's not the first time Mr Erikson has made incendiary statements.
Last year, Mr Erikson and three others were found guilty of inciting serious contempt of Muslims after staging a mock beheading to protest against the building of a mosque in central Victoria.
Also last year, he appeared in an online video calling former senator Sam Dastyari, who is of Iranian heritage, a "terrorist" and a "monkey" at a Melbourne pub.
Chelsea Beach attacks
The St Kilda incident occurred a day after a string of attacks at Melbourne's Chelsea Beach.
In a statement on Friday, Victoria Police said detectives were investigating several assaults and robberies that occurred at Chelsea Beach on Thursday night.
"The offenders were perceived to be African in appearance, aged in their late teens or early 20s," a police statement said.
Police said the group first rifled through the unattended belongings of swimmers at the beach.
A male swimmer was assaulted when he came out of the water to confront the youths before they fled with mobile phones and purses.
The group later assaulted a 28-year-old man, stealing his mobile phone, and assaulted two other men aged 25 and 30.
A 19-year-old man who was sitting on the sand was attacked with a glass bottle and assaulted with a plastic cricket bat. He was taken to hospital with non-life threatening injuries.
- Additional reporting: AAP