The 29-year-old was taken into custody on Saturday morning before being released on a $15,000 (£9,225) bond following an incident in May, when Peterson beat his four-year-old son with a tree branch, which resulted in multiple injuries to the child.
He said in a statement: "I want everyone to understand how sorry I feel about the hurt I have brought to my child. I never wanted to be a distraction to the Vikings organisation, the Minnesota community or to my teammates.
"I never imagined being in a position where the world is judging my parenting skills or calling me a child abuser because of the discipline I administered to my son.
"I am not a perfect son. I am not a perfect husband. I am not a perfect parent, but I am, without a doubt, not a child abuser. I am someone that disciplined his child and did not intend to cause him any injury. No one can understand the hurt that I feel for my son and for the harm I caused him."
The Vikings deactivated Peterson for their clash with the New England Patriots on Sunday in the aftermath of the incident.