Cooper, 25, publicly apologized Wednesday after a video surfaced of him using the racist slur at Chesney's June 9 concert at Lincoln Financial Field.
The video shows Cooper telling another person, "I will jump that fence and fight every [racial slur] here, bro."
"We are shocked and appalled by Riley Cooper's words," Eagles owner Jeffrey 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."
In a statement Thursday, the Eagles said Cooper and team officials mutually decided "his next step will be to seek outside assistance to help him fully understand the impact of his words and actions. He needs to reflect. As an organization, we will provide the resources he needs to do so."
Cooper -- an Oklahoma native who played football at Florida and was the 159th overall pick in the 2010 NFL Draft -- told reporters after the Eagles' practice Thursday he had not been able to eat or sleep after the video was made public.
"It was the toughest night I've had. It was tough, it was tough," he said.
Eagles head Coach Chip Kelly said it will "take time" for the team to get past the issue and conceded he is concerned the incident could divide the team.
"The NFL stands for diversity and inclusion," the league said in a statement. "Comments like this are wrong, offensive and unacceptable."
Cooper -- who has 46 catches for 679 yards and five touchdowns in 40 NFL games with Philadelphia -- said he was "ashamed and disgusted with myself."
"I owe an apology to the fans and to this community," he said. "I am so ashamed, but there are no excuses. What I did was wrong and I will accept the consequences."
Chesney told ESPN he was "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 said he hoped his fan base will not be judged "by one loudmouth."