An LSU spokesperson confirmed that the university and Baton Rouge Police are investigating Moore's claims.
Moore, who posted the statement on social media on Sunday, said the police officers who stopped him assumed he had a gun and drugs.
"I was violated numerous times even as going as far as trying to unzip my pants in search of a weapon that I repeatedly told them I did not have," Moore said in the statement.
When he tried to record the interaction with police, Moore said his phone was "snatched from him."
"As some celebrate the election of a new president understand the real problem have not changed," he wrote. "If I didn't tell those incompetent officers that I was a LSU football player there's no telling if I would've been here to tell the story! Yesterday wasn't a victory for America it was only a distraction."
Baton Rouge police chief Murphy Paul said the three officers have been placed on paid administrative leave while the incident is under investigation.
"We appreciate Mr. Moore bringing this incident to our attention," Paul said in a statement. "As in every case, we will be collecting all available evidence and conducting interviews. Accountability and transparency are critical in building trust with the community. I pledge a thorough investigation into this complaint."
LSU coach Ed Orgeron released a statement on Sunday night saying he was aware of Moore's "serious statements."
Orgeron wrote, "We have to listen, learn and come together to combat social injustice and racism if we are to create a safer and more equitable society for all people."
Orgeron said he met with Moore, his mother and his brother on Monday morning to learn more about what happened.
Orgeron reiterated his statement and thanked Paul for acting quickly to investigate and put the officers involved on administrative leave.
"I expect the best thing will come out," he said.
Baton Rouge mayor Sharon Weston Broome released a statement Monday that read: "My office has been made aware of a situation concerning BRPD and an LSU student. Upon notification, I have been in contact with Chief [Murphy J.] Paul; he has assured me his department is thoroughly investigating this matter and he has been in touch with the student.
"We take these allegations seriously and will await the findings of the investigation. We will get to the bottom of this situation and keep the lines of communication open with the community."
As happened at many programs across the country, LSU players held a march in late August to speak out against racial injustice in the wake of George Floyd's killing while in the custody of Minneapolis Police.