In the video, Cooper vowed to "fight every n-----" at the July concert in Philadelphia. Cooper issued an apology Wednesday afternoon.
Eagles owner Jeffrey Lurie said Cooper has been fined by the team.
"We are shocked and appalled by Riley Cooper's words," Lurie said in a statement. "This sort of behavior or attitude from anyone has no role in a civil society. He has accepted responsibility for his words and his actions. He has been fined for this incident."
The NFL also issued a statement on Cooper: "The NFL stands for diversity and inclusion. Comments like this are wrong, offensive, and unacceptable."
Eagles quarterback Michael Vick accepted Cooper's apology.
Riley's my friend Our relationship is mutual respect. He looked me in the eyes and apologized. I believe in forgiveness and I believe in him
— Mike Vick (@MikeVick) August 1, 2013
Cooper, 25, has 46 catches for 679 yards and five touchdowns in 40 career games. He is expected to assume a larger role in the Eagles' offense this year after the season-ending injury to Jeremy Maclin.
"I am so ashamed and disgusted with myself," Cooper said in a statement. "I want to apologize. I have been offensive. I have apologized to my coach, to Jeffrey Lurie, to Howie Roseman and to my teammates. I owe an apology to the fans and to this community. I am so ashamed, but there are no excuses. What I did was wrong and I will accept the consequences."
Chesney reached out to ESPN senior writer LZ Granderson about the incident and said: "All I do is get off my bus and try to give the fans all the heart and passion I got. That's where it starts and stops; that's all I think about.
"I'm as shocked as anyone to see the video of Riley Cooper that's started circulating on the internet. I don't believe in discrimination in any form, and I think using language like that is not only unacceptable, it is hateful beyond words," Chesney told Granderson.
"I don't know everything about every player who comes to our shows. We invite the teams in the places where we play, and I've found the guys from the NFL are some of the most inspiring people I meet all year. They give back to their communities, work with children, hospitals and various charities, as well as raising awesome families.
"To judge an entire audience by one loud mouth isn't fair ... not to the NFL, not to the city of Philadelphia and that awesome crowd, not to my band and crew and certainly not to me, who believes music is about bringing people together for friendship and forgetting about the things in life that bring you down. The music I make is about living life, loving life and loving everybody -- no matter who they are. That's how I was raised, and what someone else does or says doesn't reflect who I am or what my fans stand for."
Information from ESPN senior writer LZ Granderson was used in this report.