"Morkel admitted to the level 1 offence (Article 2.1.4) of using insulting language during the match," said a statement from the tournament organisers today.
The Knight Riders beat RCB in a thriller at Sharjah Cricket Stadium yesterday.
The statement added: "For Level 1 breaches of the IPL Code of Conduct, the Match Referee's decision is final and binding."
In another game yesterday, Shane Watson of Rajasthan Royals was fined USD 20 000 for maintaining a slow over rate during the Chennai Super Kings innings.