A viral video showed an interaction between Kelce and an individual outside Beaver Stadium where Penn State played Ohio State on November 2. Kelce was at the game as part of Pat McAfee's Kicking Contest put on by ESPN's "College GameDay."
The fan is heard using a homophobic slur directed at Kelce about his brother Travis, who is dating Taylor Swift. Kelce is seen turning around and grabbing someone's cell phone before spiking it to the ground.
Kelce is then heard repeating the homophobic slur towards the person.
Penn State confirmed to CNN that the investigation had been closed.
"The individual in the video footage circulating on social media has not been identified, and no one has come forward to University Police with a related complaint about damage to personal property," the school said in a statement to CNN.
Kelce apologized for the incident on ESPN's "Monday Night Countdown," and then again on his "New Heights" podcast with his brother.
"Me reacting gave him the time of day, and it also gave the situation notoriety," he said.
"That's what I regret. It didn't deserve attention. It's really stupid.
"And if I just keep walking ... it's a nothing burger. Nobody sees it. Now, it's out there, and it just perpetuates more hate.
"The thing that I regret the most is saying that word, to be honest with you. The word he used is just f**king ridiculous and it takes it to another level. It's just off the wall and f**king over the line.
"It's dehumanizing and got under my skin. ... I know now that I shouldn't have done it because now there's a video out there with me saying that word, him saying that word, and it's not good for anybody."
CNN has reached out to Kelce's representatives for comment.
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CNN's Jill Martin and Jillian Sykes contributed to this report.