A report from the Cleveland Police Department, however, blamed what it called a "riot" on the fans who were arrested, saying a security official was punched and knocked to the ground while trying to escort an unruly spectator from the stadium.
Fletcher said four of his family members were arrested and still in custody as of Monday afternoon. Cleveland police spokeswoman Detective Jennifer Ciaccia said five people were arrested for assault on a police officer, aggravated rioting and resisting arrest and that they had not been officially charged by Monday evening.
Fletcher, who is from Cleveland, said he had about 50 friends and family at the stadium for Washington's 38-21 win Sunday. He said they were harassed because they were wearing Redskins colors, but he said the fracas apparently began when a security official was asking how the large group had acquired such good seats.
"What led to the whole ruckus was something that happened with stadium security," he said. "As opposed to diffusing the situation, they were more instigators. They didn't diffuse the situation. It wasn't even with the fans at that point in time. I think one of the stadium workers, he went overboard with what his job responsibilities were."
The police report said the incident began when a security officer saw a fan who claimed to be related to Fletcher taunting Browns fans. When the officer later tried to eject the fan, others became involved and that one fan punched the officer, "knocking him to the ground."
The report says later "the riot moved into the concourse area" and that several people were treated for injuries. Fletcher also said he had an aunt who was hospitalized for "neck injuries" and released.
Tenable Protective Services coordinates security at Cleveland Browns Stadium. A team spokesperson told ESPN.com that the Browns still are investigating the incident.
"We are still in the process of collecting all of the information regarding the incident from the various security groups who work the games, including Cleveland Police and Tenable," the spokesperson told ESPN.com.
John Lloyd, operations manager with the stadium's Tenable security contractor, had no comment.
Fletcher told "NFL AM," an NFL Network program, that his family members were confronted by Browns fans in the parking lot prior to the game.
"It's my understanding from the moment they got out of their car, they were harassed by Browns fans and things like that -- even all the way up into the stadium," Fletcher said. "I had a 13-year-old cousin who was hit in the face prior to the game. This was going into the game, I guess, in the tailgate area. So a lot of harassment that took place prior to the game and during the course of the game."
Fletcher, 37, described the incident as "disheartening" and did not rule out pursuing legal action, telling "NFL AM" that his family "would like to see something done."
Fletcher, Washington's leading tackler, recorded seven tackles Sunday as the surging Redskins (8-6) pushed into a three-way tie atop the NFC East.
"It was an unfortunate situation," he said. "Put a damper on an otherwise great homecoming, being able to get a win and things like that. It was definitely not a good finish to the game."
ESPN.com's Jamison Hensley and The Associated Press contributed to this report.