The New Orleans police said in a statement the warrant involved a charge of alleged simple battery.
After watching his former side Louisiana State University beat Clemson University at the Mercedes-Benz Superdome in New Orleans on Monday, Beckham joined the team in the locker room, where he was seen dancing and celebrating with players.
One video that surfaced online showed the 27-year-old appearing strike a locker room guard on the behind.
A Browns statement on Thursday said: "We are aware of the incident and have been in touch with Odell and his representatives on the matter.
"They are cooperating with the proper authorities to appropriately address the situation."
Beckham was selected by the New York Giants in the first round of the NFL Draft in 2014, before moving to the Browns in 2019.