Ball stamped on Ronaldo during the first-half of City's defeat to United at the weekend.
"I deeply regret what I did and have accepted the FA's charge without hesitation. I have also sent a personal apology to Cristiano," Ball told the club's official website.
"My action should not be seen on a football pitch and I know we have a responsibility at Premier League level to set a good example to the whole football community.
"I am proud of my disciplinary record and have never been sent off in my professional career."
Ball will automatically receive a three-match ban when a disciplinary commission sits to hear the case on Thursday - although he could be served with a longer sentence.