The son is 4 years old, KHOU-TV in Houston has reported.
The CBS affiliate cites text messages that reportedly include a photo of the son with an apparent head wound covered by bandages.
Peterson was indicted by a grand jury on charges of reckless or negligent injury to a child on Friday.
In a statement on Monday, Peterson apologized for "the hurt I have brought to my child." He said he will testify in court he did not intend to harm his son and said that he is not "a child abuser."
The Houston TV station reported the mother of the 4-year-old -- from a different mother than the child he stands charged with abusing -- filed a report with Child Protective Services.
No charges have been filed so far against Peterson in this latest alleged incident.
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