Peterson is the star player of the Minnesota Vikings and recently played for them in London against the Pittsburgh Steelers.
Sioux Falls police spokesman Sam Clemens said the boy died after he suffered injuries doctors believe were caused by child abuse.
The boy, whose name was not released per the family's request, was believed to have suffered injuries from an alleged assault by a man the boy's mother was dating. The child was in critical care at a South Dakota hospital before his death.
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.
The alleged assault took place Wednesday evening when Sioux Falls police responded to a 911 call for a child who was choking. Officers found the unresponsive child and transported him to a nearby hospital. Doctors determined that the child’s injuries were consistent with abuse and that they were not accidental.
Patterson was arrested the night of the incident. The boy's mother was not at the apartment at the time of the incident, according to police. Local police did not release the names of the parents, citing that it was not part of their investigation.
Peterson took to Twitter to thank those who had passed on their sympathies.
"Thank you to my family, my fans and fans of other teams for their support," he wrote.
"The NFL is a fraternity of brothers and I am thankful for the tweets, phone calls and text messages from my fellow players.
"God Bless everyone and thank you so much."
When the child was in critical condition Peterson said he would definitely still play for the Vikings in this Sunday's match against the Carolina Panthers but the tragic developments since then make this unclear.
Head coach Leslie Frazier said the decision to play Sunday at home against the Carolina Panthers would be entirely up to Peterson.
"We'll see how things go with him," Frazier said. "We expect him to play, but this is a very personal situation that he's dealing with."
This is the latest in a long line of personal tragedies for Peterson. At the age of eight, Peterson witnessed his older brother being struck on his bicycle and killed by a drunk driver. In high school, Peterson’s father was sentenced to 10 years in prison in a drug-related case. Peterson’s stepbrother was killed by a gunshot in Houston while Peterson was preparing for the NFL draft at the scouting combine.