Police are not releasing the boy's name out of respect for the family, but Peterson's father, Nelson Peterson, told the St. Paul Pioneer Press the child is Adrian Peterson's son.
Lincoln County State's Attorney Tom Wollman confirmed the death of the child, who had been in critical condition in a hospital with severe head injuries since Wednesday. The boy died at 11:43 a.m. at Sanford USD Medical Center in Sioux Falls after being removed from life support, Wollman said.
Joseph Patterson, 27, was charged with aggravated assault and aggravated battery in the child's death. He had a court appearance Friday and was ordered held on $750,000 cash bond.
Wollman said he'll review police and medical reports before making further decisions about criminal charges, possibly by early next week.
Peterson tweeted a series of messages Friday night, thanking his family, friends, fans and fellow NFL players -- whom he referred to as "a fraternity of brothers" -- for their support.
Peterson took to Twitter again on Saturday morning, confirming that the 2-year-old was not Adrian Peterson Jr.
My son Adrian Jr. who lives w/me is healthy. Appreciate the concern. We respectfully ask to stop tweeting his pics.— Adrian Peterson (@AdrianPeterson) October 12, 2013
We are currently not posting photos of my son who passed away. Thank u for your understanding.— Adrian Peterson (@AdrianPeterson) October 12, 2013
The Vikings (1-3) host the Carolina Panthers (1-3) on Sunday.
Peterson, speaking to reporters at the Vikings' team facility Friday before an announcement about his son's death had been made, said he would play Sunday.
A Vikings source, however, told ESPN's Josina Anderson that that feeling "was the emotion of the moment. That could change."
Peterson left the team facility Friday evening.
"I think we should allow Adrian to grieve tonight," the source told Anderson. "The plan is to talk to him tomorrow for now."
An additional source close to Peterson told Anderson he was certain the running back would play against the Panthers. Another source close to the player said he would tell Peterson to sleep on it.
Police and an emergency medical services crew were called Wednesday to a Sioux Falls home, where the child was found unresponsive and was rushed to the hospital, according to a police statement. The child was under Patterson's care at the time, and nobody else was at the home.
At the hospital, it was discovered that the child's injuries were consistent with abuse. Patterson, who police say is the boyfriend of the child's mother, was taken into custody and charged.
Peterson is second in the NFL with 421 yards rushing and first in the league with five touchdowns. He came back from reconstructive knee surgery to rush for 2,097 yards and win the league MVP award last season.
The Panthers, Sunday's opponent, were sympathetic.
"It's absolutely terrible. Our thoughts and prayers go out to him and his family, and hopefully things work out," coach Ron Rivera said.
Vikings coach Leslie Frazier said he thought Peterson practiced as well as he could Friday considering the circumstance.
"He seems like he was into it, engaged in what he had to get done," Frazier said. "Obviously, tough. He's human. But he was into it mentally, best as he could be."
Fellow running back Toby Gerhart said: "It's hard for any man to admit that he's hurting or he needs help or anything like that. For us to be around him and tell him we've got his back, if there's anything he needs that we're there for him, I think that goes a long way."
News of the boy's death spread throughout the sports world Friday.
"He's a friend of mine, first of all," James said. "I've had a pretty good relationship [with] him for a long time. I respect him as a father and as a role model. And also having two boys of my own, it hit home. It sucks that this has happened. Like I said in my tweets, my family, our prayers go up to him and him and his family, his son.
"I'm absolutely angry, because it's an innocent kid that's taken away by someone's stupidity. I don't know the guy who did it. But there's nothing that a 2-year-old kid can say, can do, can harm to any grown-up that would make them do that. It's a lot of hurt. It's a lot of anger. It's messed up."
Information from ESPN.com Vikings reporter Ben Goessling, ESPN.com's Michael Wallace and The Associated Press was used in this report.