Ball and Fulham's Michael Brown were both charged with violent conduct after separate incidents in last weekend's Premier League matches.
Ball stamped on Ronaldo as the Portugal winger lay on the pitch following a challenge in Saturday's game at the City of Manchester Stadium.
The incident was missed by the referee but caught by television cameras. United won the game 1-0 with a Ronaldo penalty -- awarded after a foul by Ball on the United winger.
"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 City's Web site (www.mcfc.co.uk).
"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."
Brown's charge follows an alleged head-butt on Liverpool's Spanish midfielder Xabi Alonso during Fulham's 1-0 win at Craven Cottage on Saturday.
Liverpool manager Rafa Benitez said after the game: "It's clear for everybody to see this incident and how the officials didn't see it is unbelievable."
The FA said in a statement the two players had until 1700 GMT on Wednesday to respond to the charges "which carry an automatic three-match suspension and the cases will be heard by a Disciplinary Commission on Thursday."
