An 11-year-old and a 12-year-old were targeted by the white van in the daylight attempted attack on Woodside Park, just off Avenue Road in Dudley.
The children were playing football when they were assaulted by another group of youngsters before being driven at by the van.
WATCH the footage:
Footage posted on Spotted: Brierley Hill and local Facebook page
A video of the incident, which has been posted to social media, shows the van speeding towards the children before swerving and attempting to hit them.
It comes after Dudley Council has been working to evict an illegal travellers camp from the site, which has been set up for more than a week.
Police have now launched an investigation following the incident on Monday (August 27) – which saw the two children suffering minor injuries.
A West Midlands Police spokesperson said: "An investigation has been launched following reports two children were driven at by a white van at Woodside Park, just off Avenue Road in Dudley.
"The youngsters, aged 11 and 12, had been playing football in the park when they were assaulted by another group of youngsters, and driven at by the van on Monday 27 August.
"The children suffered minor injuries in the assault. Footage of the incident has been obtained by police.
"Anyone with information can contact us via Live Chat at west-midlands.police.uk between 8am to 9pm, call 101 or contact Crimestoppers anonymously on 0800 555 111 quoting crime number 20DY/195682V/18."
Councillor Patrick Harley, leader of Dudley Council, said: “I can confirm that travellers have moved on from Woodside Park. We have already moved on to the site to carry out clean-up operations.
“I share people’s frustrations with the legal process we have to go down to remove travellers. It is for this reason we are continuing to work towards a temporary site in the borough to speed up the process of getting them removed, and potentially stop them visiting in the first place.
“We were made aware of a video circulating on Facebook. While it is a police matter – and we passed it on to them as soon as we were made aware of it – clearly no right-minded person can see such behaviour as acceptable.
“We remain committed to setting up a temporary travellers’ transit site in Coseley which will allow us to move travellers off Woodside and other parks within hours, rather than weeks.”
He added: "If Labour politicians hadn't tried to prevent the installation of a travellers site then none of the affected areas would have suffered for more than two hours.
"Failure by travellers to either move out the borough or onto the site would have meant arrest and vehicles being compounded by police.
"Hopefully when the minister finally gives us the all clear then residents will no longer suffer this annual trespassing on our open spaces."