The clip, which has been shared more than 8,000 times on Facebook, showed four guards pinning the man to the floor following an incident in the mall's food court area earlier this month.
The footage shows two guards sitting on top of the dark-clothed male who can be heard screaming out as the guards sit on top of him to restrain him.
Two more guards come to their colleagues' aid as the man's head is jerked violently backwards into the ground as they wrestle him to the floor.
But the Frenchgate Centre has said the man shown in the clip has now said sorry for the incident on October 5 which led to police being called.
Paddy Mellon, general manager at Frenchgate Shopping Centre, said: "The incident was resolved with the assistance of South Yorkshire Police and our security team have received an apology from the gentleman involved for his behaviour which led to the police being called.
"We are currently carrying out an internal investigation into this matter and at this time we cannot comment further.”
The centre added that the incident involved two adult males and four of the centre's security staff.
The Free Press has seen the video at the centre of the argument.
The video, was shared by Jack Harris Clarke on Facebook earlier this month with the message: "This young lad was brutally taken down by four security guards in Doncaster Town Centre.
"He was called names before being pinned to the floor. He couldn't do anything and one of the security guards slammed his head on the floor as shown in the video.
"Many people were surrounding this incident and an elderly women was told to "stay the f*** out of it."
"This behaviour shouldn't be used in such a public place! Please share to show how disgusting the security guards are in Frenchgate Shopping Centre."
It is understood the man at the centre of the clip had been asked to leave the centre for earlier behaviour.
In the footage, the man is heard screaming: "I can't breathe!" as he is restrained. One of the guards can be heard telling him: " When you are asked to leave, you go - no arguing, just go."
One of the guards can also be heard telling the man to "calm down" as the fracas continues with the man attempting to wrestle free.
A voice off camera can be heard shouting: "Get off his face, you've got your knee in his face. It's f***ing illegal. He's hurting a child!"
The guards can also be seen telling shoppers to move along, with one saying: "Nothing to see. Move away."