Paul Serbu, 62, of Franklin, Ohio, had been charged with disorderly conduct in a Pikesville, Maryland, cemetery after a video of the incident appeared on YouTube over the summer.
Baltimore County Deputy State's Attorney John Cox told The Baltimore Sun that prosecutors decided to drop the charges after receiving information about a physical condition that Serbu has and several conversations with David Modell, the son of the former Ravens owner. Cox said it would be inappropriate to elaborate on Serbu's condition.
Serbu has agreed to appear on David Modell's Baltimore radio show to discuss what happened.
Serbu could have faced up to two years in jail and a $500 fine.
In the online video, which was titled "Browns Fan Pays Respects to Modell," Serbu arrives at the gravesite dressed in an Ed Reed jersey. He 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.
Art Modell died in 2012 at the age of 87. He spent 43 years as an NFL owner, overseeing the Browns from 1961 until he moved the team to Baltimore in 1996, when they became the Ravens.
The Associated Press contributed to this report.