The black South African striker squared up to Mijailovic at the  end of Blackburn's 2-1 UEFA Cup win at Polish side Wisla Krakow a  week ago after being allegedly provoked by the defender.
  
McCarthy and another player who overheard the abuse had made a statement on the incident which was forwarded to UEFA and the English Football Association.
  
Reports claim that McCarthy had mentioned the abuse to Swedish referee Stefan Johannesson at half-time during the match, but to no avail.
  
UEFA's Control and Disciplinary Body handed down the ban on Thursday.
  
"UEFA launched the inquiry on the basis of an official complaint submitted by Blackburn, as well as on the basis of an additional report submitted by the match referee," UEFA said in a statement.
  
"The UEFA disciplinary body, in reaching its decision, repeated its view that racism not only constituted a serious breach of the fair play principle, but also presented a serious threat to sport and its ethical values."
  
English Premiership side Blackburn applauded UEFA's swift response to the incident.
  
"Firstly, we appreciate UEFA's speed in dealing with this important issue," the Lancashire club said in a statement.
  
"Secondly, we believe that UEFA's decision sends out a clear message that racism will not - and should not - be tolerated in the game."
  
Mijailovic, 24, has until Monday, October 30 to appeal against the ruling.