The unidentified man in the video, titled "Browns Fan 'Pays Respects' to Modell," arrives at the gravesite dressed in a Baltimore Ravens Ed Reed jersey.
He then pulls it off to reveal a Browns Lyle Alzado No. 77 jersey and apparently urinates on Modell's grave out of the bottom of his pants leg using a catheter.
Afterward, he speaks to the camera.
"You know, Art, when you ... tried to kill the Cleveland Brownie, you didn't do so good, the Browns fans wouldn't let you, you piece of s---," he says. "I'm in rat land, and I'm going to use the words you used a few years ago.
"As far as pissing on your grave, I had no choice."
When Modell moved the team to Baltimore in 1996, he said he had "no choice."
The video has received more than 10,000 hits. A spokeswoman for the Druid Ridge Cemetery told The Baltimore Sun that the Browns fan's decision to urinate beside Modell's grave was "disappointing and disrespectful."
Police did not immediately respond to the paper on the situation and its legality.
Modell died in 2012.