Harbhajan, who won man-of-the-match for his all-round performance, was found guilty of abusing Suman and was fined $15,000 for the level 1 offence.
Match referee Sundar Raman imposed the punishment after Harbhajan gave Suman a verbal send-off on claiming his wicket.
Harbhajan had a very good match on Sunday, first smashing a quick-fire 49 off 18 deliveries to push Mumbai Indians' total to 172 and later coming good with the ball and ending with figures of 3 for 41.
Mumbai Indians next face Kings XI Punjab on Tuesday.
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