Three other men have also been arrested after the 29-year-old woman said the officers bundled her into a car as she was leaving an upmarket hotel in India's financial capital on April 3.
Deputy commissioner Dhananjay Kulkarni said the woman has alleged she was then driven to a police outpost and raped by the officers before they extorted up to 500,000 rupees ($7,800) from her.
"The investigations are being done meticulously considering the involvement of police and nature of the crime," Kulkarni told AFP.
"Right now, the allegations of extortion seem genuine, but the matter of sexual assault cannot be confirmed at this moment."
"They (the policemen) had no business to be there" outside the hotel, he also said.
Local media have reported that the woman's friend had gone to the police station to deliver the money after travelling to several ATMs in the night.
The woman reportedly sent a text message to Mumbai's police commissioner Rakesh Maria several days later alerting him to the incident, before meeting him to give more details.
India introduced tough laws against sex offenders in the wake of the fatal gang-rape of a Delhi student in the capital in December 2012 that sparked mass street protests.
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