Peterson was processed at the Montgomery County jail and released on USD 15,000 bond, according to a sheriff's office spokesman, Lt. Brady Fitzgerald.
He is charged with causing injury to a child age 14 or younger, allegedly by spanking one of his sons with a tree branch, on or around May 18.
Peterson, widely considered the best running back in the NFL, won't play on Sunday in Minnesota's home opener against the New England Patriots.
Brian McCarthy, a spokesman for the league, said Peterson's case "will be reviewed under the NFL's personal conduct policy."
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Peterson's attorney, Rusty Hardin, said his client "has never hidden from what happened" in the case.
"Adrian is a loving father who used his judgement as a parent to discipline his son. He used the same kind of discipline with his child that he experienced as a child growing up in East Texas," Hardin said yesterday.
He said Peterson cooperated fully with the investigation, voluntarily testifying before a grand jury for hours.
Peterson's arrest came with the NFL facing criticism for its handling of a domestic violence case involving former Baltimore Ravens running back Ray Rice. Now the league has another public relations problem with the charge of child abuse against an even bigger star in Peterson.
Commissioner Roger Goodell announced tougher penalties last month for players accused of domestic violence: Six weeks for a first offence and at least a year for a second violation.