According to KWTX-TV of Waco, Texas, Nielsen was arrested three days later and charged with misdemeanor assault with bodily injury.
He was freed on bond and hasn't attended the Bears' past two football games against Oklahoma and Kansas State.
Baylor officials declined to comment on Monday night, saying they don't talk about personnel matters.
According to an arrest warrant obtained by KWTX-TV, Nielsen confronted reporter James McBride on the field while he was taking a photograph with an unidentified Baylor player.
McBride, who writes for The Blaze News in Keller, Texas, told police that Nielsen grabbed him by the throat with his right hand, squeezed and pushed him away from the football player.
The warrant said McBride had visible scratches on his neck and complained of pain around his throat.
The warrant said photographs were taken of McBride's injuries, and security cameras at McLane Stadium recorded the incident.
"I had asked the player if I could take a photo with him [and] he said yes," McBride told KWTX. "I was leaning back to take the photo. I heard somebody who I didn't know at this point in time yell from my right-hand side, saying 'no interviews on the field.'
"About that time, they came in and tomahawk-chopped, trying to knock the phone that I had taken the picture with out of my hand. They were unsuccessful in trying to do that, and when they couldn't do that, they came up and they grabbed my throat, and I pulled back. Whenever I looked up, I saw that it was Heath Nielsen."
Right after the incident, McBride said Nielsen told him, "You'll never [expletive] work in this business again. You're abusing your privileges on the field."
Nielsen has worked the past 17 years at Baylor, and his job duties include working directly with the Baylor football program and media. According to the school's website, Nielsen is "responsible for management of the public image of the program. Nielsen is the program's spokesman, the liaison between local and national media, and the primary contact with television and radio networks that broadcast Baylor games."
In October 2014, the Big 12 publicly reprimanded him for Twitter comments about officiating during the Baylor-West Virginia game. The conference fined the school $1,000 for his comments.