Clough, 63, had been accused of misconduct for allegedly accepting unauthorised payments in transfer deals following the publication of the findings of the lengthy investigation.
But the FA said in a statement that "it would not be in the best interests of the game to pursue the misconduct charge against Mr Clough because of his poor health."
The statement continued: "Mr Clough has provided medical evidence which indicates that he is unfit to attend a personal hearing. The FA considers that in all the circumstances, Mr Clough would not be able to present his defence to the best of his ability and it would be in no one's interest to continue the prosecution."
However, similar outstanding misconduct charges against Ronnie Fenton, the former Forest assistant manager, and Steve Burtenshaw, the former chief scout at Arsenal, are still due to be heard on 16 September.
Charges against Nottingham Forest Football Club arising out the inquiry will also be heard by an FA disciplinary commission on a date to be confirmed.