The German Football Association (DFB) have absolved the Bavarians of any wrongdoing and blamed the match officials for the mix-up.
Bayern Munich won the game 4-1 to enhance their push for a tenth straight Bundesliga title while Freiburg's Champions League ambitions took a hit with the defeat.
Freiburg launched an appeal to have the result overturned which has proven to be unsuccessful.
The controversial moment occured in the 85th as Bayern led 3-1 when they messed up a substitution.
Bayern prepared a double substitution but Kingsley Coman remained on the field as his old number 29 was held up instead of the current 11.
The mix-up saw Marcel Sabitzer enter the field of play with Coman still on the pitch and the game continued for 17 seconds before the error was realised, leading to a lengthy delay to sort things out.
"The DFB sports court has decided Bayern Munich cannot be blamed for the introduction of a non-eligible player," the DFB said in a statement.
"It is more down to the mistaken behaviour of the officials that a 12th man was introduced and the game continued."
Stephan Oberholz, chairman of the DFB sports court, said: “First of all, we assume that all FC Bayern players were eligible to play.
“Regardless of this, the at best slight contribution to misconduct by Bayern, which is secondary to that of the referees, is also insufficient from a point of view of proportionality to justify the serious legal consequences of a game revaluation.”
He added on the role played in the confusion by appointed match officials: “They didn't fulfil their obligation to check the number of players.
“In the end, the referee continued the match without checking the permitted number of players again.”
Bayern Munich have a nine-point lead over second placed Borussia Dortmund with six games left to play.
