The video, which was taken in a play area in West Park, Wolverhampton, shows a group of young men shouting racist abuse and threatening to stab members of a Muslim family on Saturday, June 5.
It also shows two of the group getting physically aggressive, with one of them hitting the phone out of the hands of the person taking the video.
West Midlands Police confirmed on Twitter that it was investigating the attack, which happened around 8.30pm.
The force asked that the video is not shared on social media, and that anyone with information gets in touch as soon as possible.
A spokesman said: "We are investigating a racial attack on a family at a park on Park Road West, Wolverhampton at around 8.30pm on Saturday 5 June.
"We have since been made aware of a video of this incident circulating on social media, which we are also investigating.
"We take reports of this nature incredibly seriously, and will not tolerate this kind of abuse in our communities.
"We are working to identify the people responsible and ask that people do not continue to share the video, as this may cause further upset to the family involved.
"Anyone with information can contact us quoting log number 3816 of 5 June."