The IPL said that the fine has been imposed as it was MI's first offence of the season.
"As it was his team's first offence of the season under the IPL's Code of Conduct relating to minimum over rate offences, Mr Sharma was fined Rs 12 lakh," it said.
MI fell to their second defeat in four matches on Tuesday, losing to DC by six wickets. Veteran spinner Amit Mishra's four-wicket haul helped DC restrict the mighty MI batting lineup to a score of 137/9. DC then took their time in chasing down the target, eventually scoring 138/4 with five balls to spare.