Yorkshire had a player named Michael Vaughan from 1993 to 2009.
The former England captain won't be involved in the coverage of the Aussies.
The 47-year-old, who was stood down from his Radio 5 Live show earlier in November, will not be involved in the BBC's wider coverage of the sport at the moment.
He has denied the allegation many times.
The first of five Tests between England and Australia will take place on December 8 in Brisbane.
The Test Match Special radio team has a summariser named Michael.
"While he is involved in a significant story in cricket, for editorial reasons we do not believe that it would be appropriate for Michael Vaughan to have a role in our Ashes team or wider coverage of the sport at the moment," the statement said.
He has a conflict of interest because he is involved in the Yorkshire story.
Azeem Rafiq said that during a County Championship match in 2009, he and three other Yorkshire players were told "too many of you lot, we need to do something about it".
Rafiq's account was supported by Rana Naved-ul-Hasan and Adil Rashid, who said they heard the comment.
The fourth player in the group, bowler Ajmal Shahzad, told the Daily Mail that the senior guys were good to him.
In his Daily Telegraph column, he denied making the comment.
"I categorically deny saying the words attributed to me by Azeem Rafiq and want to re-state this publicly because the 'you lot' comment simply never happened," said the statement made earlier in November.
It is upsetting that a former team-mate made a false accusation against me, and that two other players supported him.
I have been in contact with six other players from that team and none of them have any recollection of what was said.
Rafiq was critical of Vaughan when he appeared in front of the committee.
Rafiq said that it was important for Michael that we didn't make it all about him.
