The 29-year-old was indicted on charges of reckless or negligent injury to a child, and was taken into custody on Saturday morning before being released on a $15,000 [£9,225] bond.
In the aftermath of his dealings with the authorities, the Vikings have taken the decision to leave him out of their side for the clash against the Patriots at TCF Bank Stadium.
Following his indictment, Peterson's lawyer Rusty Hardin said in a statement: "He used the same kind of discipline with his child that he experienced as a child growing up in East Texas.
"Adrian has never hidden from what happened. He has cooperated fully with authorities and voluntarily testified before the grand jury for several hours. Adrian will address the charges with the same respect and responsiveness he has brought to this inquiry from its beginning."
Peterson was voted MVP of the NFL in the 2012 season.