"I should start off by saying I really appreciate all the support that I've been receiving from fans, the Vikings organization," Peterson said Friday afternoon. "This is a private matter and I would ask you all to please just respect my privacy and not ask at all about the situation at hand. Thanks."
Peterson's father, Nelson Peterson had told the St. Paul Pioneer Press that the child is Adrian Peterson's son.
"All I can say is, we are asking for prayers and for respect for our family as we deal with this tragic situation," Nelson Peterson said.
Joseph Patterson, 27, is being held on two felony counts of aggravated battery of an infant and aggravated assault domestic. He was in court Friday for a probable cause hearing where bail was expected to be discussed.
Peterson, who spoke to reporters Friday at the team's facility, said he will play Sunday. The Vikings (1-3) host the Carolina Panthers (1-3). Coach Leslie Frazier said he and Peterson will "talk more over the next 24 hours."
"I really appreciate all the support from fans and the Vikings," Peterson said. "I ask y'all to respect my privacy."
Police and an EMS crew were called to a Sioux Falls home Wednesday 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.
On Friday, Peterson said: "I will be playing Sunday, without a doubt."
Vikings coach Leslie Frazier was less definitive.
"We expect him to play but this is very personal situation he is dealing with," he said. "We'll talk to him more in the next 24 hours."
As for coping with a stressful situation, Peterson said playing helps.
"You know, football is something I will always fall back on. It gets me through tough times," he said. "Just being around the guys in here, that's what I need in my life, guys supporting me and just being able to go out and play this game I love. Things that I go through, I've said a thousand times, it helps me play this game to a different level. I'm able to kind of release a lot of my stress through this sport, so that's what I plan on doing."
He added: "One thing I always go back to is the good Lord never gives you more than you can handle. So I'm built tough."
Peterson was on the field for stretching with the Vikings on Friday morning. He left for the locker room briefly during special-teams drills, which he doesn't participate in, and returned later.
"It's a cliche to say you've got each other's backs on a football team, but in a situation like this, it's a testament to a football team being a family," backup running back Toby Gerhart said.
Peterson is second in the NFL with 421 yards rushing and first in the league with five touchdowns.
ESPN.com Vikings reporter Ben Goessling contributed to this report.