The child's death was first reported by the Minneapolis Star-Tribune and confirmed by Reuters.
Peterson returned to practice Friday, but did not directly address reports regarding his son.
Peterson missed practice Thursday to deal with a medical issue involving a young family member.
"I really appreciate all the support that I've been receiving from fans, the Vikings organization," Peterson said. "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. Appreciate it."
Peterson said he will definitely play Sunday's game against the visiting Carolina Panthers.
"Football is something I will always fall back on," he said. "It gets me through tough times. 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."
Peterson's father, Nelson Peterson, told the St. Paul Pioneer-Press earlier Friday that the child is one of Peterson's sons.
The Argus (S.D.) Leader reported that Peterson was spotted in Sioux Falls Thursday and that the health issue he was tending to was "very serious" and "likely will be a police matter." At that time, a Sioux Falls toddler was in critical condition with choking injuries after allegedly being assaulted by a man.
TMZ first reported Friday that the incident involves Peterson's 2-year-old son. He was reportedly rushed to a hospital and medical experts determined the injuries were consistent with abuse.
According to police, emergency responders arrived at the apartment where Peterson's son reportedly lives at 5:46 p.m. Wednesday and found the child unresponsive.
Joseph Robert Patterson, 27, was being held on bail set at $750,000 in cash at the Minnehaha County Jail. He was charged with aggravated assault and battery of an infant.
Police spokesman Sam Clemens told the Star-Tribune the state attorney's office is reviewing the case to consider additional charges against Patterson.
"We're surrounding our investigation around the injuries to this child," Clemens said. "Who the father is does not come into play in this investigation."
Police said the child was in Patterson's apartment, where the boy had recently moved with his mother. The child's mother recently began a relationship with Patterson.
Patterson has a prior domestic abuse record involving a different woman and child. He pleaded guilty to simple assault in an incident last year.