"I accept my fine, I'll pay it, and move on," Green said. "I did something I wasn't supposed to do, so now I have to accept the consequences and that's fine."
The fine was the second in the career of the Pro Bowl wideout, who was docked $5,787 for kicking a ball into the stands after scoring a touchdown in 2015.
Sunday's fireworks began late in the second quarter as Ramsey shoved Green to the ground after the whistle blew on a 1-yard run by Cincinnati rookie running back Joe Mixon.
Green erupted, grabbed Ramsey by the neck from behind and slammed him to the ground. The 29-year-old then delivered several punches to Ramsey until a group of players jumped into the fray.
Both benches cleared, and it took several minutes before order was restored.