Cheerleaders have been brought in from all over the world
Indian police say the organisers of the new tournament transforming world cricket could be fined if cheerleaders are deemed to be dressed indecently.
The cheerleaders have been introduced into the Indian Premier League as part of moves to add glamour and entertainment to the game.
Some politicians say the cheerleaders are "vulgar and obscene".
Mumbai police say they will be checking that the cheerleaders' performances do not violate entertainment licences.
The cheerleading girls, wearing short skirts and low-cut tops, have been hired from around the world to perform during the matches which are also being heavily endorsed by leading Bollywood stars.
They include cheerleaders from the Washington Redskins.
'Lines of decency'
Ram Rao Vagh, the police commissioner for New Mumbai, a suburb of Mumbai, where the home team is hosting five matches starting on Sunday, told the BBC that they were not considering any action against the cheerleaders themselves.
"It is difficult to enforce moral policing, we cannot define vulgarity always. It is difficult to ascertain what is vulgar and obscene," Mr Vagh said.
But he said the organisers could be fined for violating the norms of the entertainment licence they had secured for allowing performances in the stadium.
Senior officers would decide whether the cheerleaders had crossed the "lines of decency".
A spokesman for the local team, the Mumbai Indians, said they were not worried.
"Our cheerleaders are properly dressed. They are within limits of what our culture permits. So we have no problems," Javed Akhtar told the BBC.
However, the junior interior minister of western Maharashtra state, of which Mumbai is the capital, said the performances of cheerleading girls at the Indian Premier League matches were "absolutely obscene".
Cheerleaders have complained of sections of the crowd jeering at them Pic: Sandipan Chatterjee/Indian Express
"We live in India where womanhood is worshipped. How can anything obscene like this be allowed?," Siddharam Mehetre told the Press Trust of India news agency.
"This thing is meant for foreigners and not for us. Mothers and daughters watch these matches on television. It does not look nice."
Many others find the indignation misplaced, coming from a city, which is home to a thriving industry of Bollywood films where dance sequences featuring women in skimpy dresses are routine.
Bollywood actor, Shah Rukh Khan, who also owns one of the teams in the competition, is one of them.
"What's wrong with cheerleaders? I am also a family person, I do not see anything negative in it," he said.
The head of India's National Commission for Women said there was nothing wrong with the cheerleaders if it "just for adding entertainment to the game".
"It has to be presented in the right manner keeping Indian values intact," said Girija Vyas.
A former Bollywood actor and a politician belonging to the opposition Bharatiya Janata Party (BJP), Shatrughan Sinha said the cheerleaders were making a "mockery" of the game.
There have been reports in the Indian newspapers of cheerleaders complaining of sections of the crowd jeering at them and making lewd comments.