Pollard and Starc clashed during MI's innings in the 17th over. The West Indies pulled out of his batting stance but Starc, who was in his run-up, bowled the ball towards him.
Angered by this, Pollard hurled his bat towards Starc but luckily it did not go far away and fell at the batsman's feet.
A media release from IPL organisers said that the match referee Andy Pycroft imposed 75 (Pollard) and 50 (Starc) per cent fines of their match fees on both players.
"Kieron Pollard of Mumbai Indians and Mitchell Starc of Royal Challengers Bangalore were both fined after an incident in the first innings," the statement said.
"Mr Starc admitted to the level 2 offence (Article 2.2.11) of conduct contrary to the spirit of the game and accepted the sanction of a fine of 50% of his match fee.
Mr Pollard admitted to the level 2 offence (Article 2.2.7) of throwing his bat at or near a player and accepted the sanction of a fine of 75% of his match fee," it added.
Also for the same match, both captain Rohit Sharma of MI and RCB's Virat Kohli were fined for mainting slow over rates.
"Rohit Sharma of Mumbai Indians and Virat Kohli of Royal Challengers Bangalore were both fined after their team maintained a slow over rate. As this was Mr Sharma's second slow over rate offence of the season, he was fined Rs. 24 lakh. Each of the other ten members of the Mumbai Indians team was fined the lesser of Rs. 6 lakh or 25% of his match fee. Since it was Mr Kohli's first slow over rate offence of the season, he was fined Rs. 12 lakh," the release said.
Also, Varun Aaron of RCB was reprimanded after he violated article 2.1.1 of the Code of Conduct for a breach of paragraph 4.2 of the IPL Clothing Regulations.