The case was filed on the basis of a complaint from a 33-year-old woman from Bihar, a former bar dancer, who has alleged that Binoy Vinodini Balakrishnan sexually assaulted her promising marriage and that she has an eight year old son from him.
Admitting that he knew the woman, Binoy, however, said the allegation was "baseless".
Six months ago, the woman had sent a letter to him demanding Rs five crore and alleging that he had married her and had a child from her, Binoy told television channels in Thiruvananthapuram.
"I got married in 2008. There is no need for me to keep it under wraps. This is a blackmailing ploy from the complainant," he said.
Binoy said he filed a complaint in May against the woman with the Inspector General of Police, Kannur range.
The complaint was forwarded to then Kannur Superintendent of Police (SP) G Siva Vikram for further action.
But with the Lok Sabha polls going on and due to jurisdiction issues, no further action could be taken, police sources told PTI.
Binoy said the Mumbai police had not got in touch with him so far and that he was prepared to face the case legally.
Based on the woman's complaint, Binoy has been booked under Indian Penal Code (IPC) sections 420 (cheating) and 376 (rape), Oshiwara police station's senior inspector Shailesh Pasalwad said in Mumbai.
The complainant had got acquainted with the accused some years ago when she used to work as a bar dancer in Dubai, he said.
The accused used to frequently visit the dance bar and the woman got into a relationship with him, the officer added.
She was asked to quit her job by Binoy, who had promised to marry her, he said.
The woman, in her complaint, mentioned that in 2010, the accused had rented a flat in Mumbai's Andheri, where he used to visit her regularly, and that she had a child from the relationship.
The woman also claimed that she came to know last year that the accused was already married, following which their relationship turned sour.
She also alleged that the accused threatened her with dire consequences.
Last year, a travel ban was imposed on Binoy by a Dubai court in connection with a cheating case filed by the Gulf-based JAAS Tourism, which alleged that he had cheated the company of Rs 13 crore.
Meanwhile, senior CPI(M) leader and Polit bureau member, Brinda Karat maintained that the party had nothing to do with the case.
"The CPI(M) has got nothing to do with the case. Let the individual against whom the case has been filed prove if it is correct or not", Karat told reporters at New Delhi.
Asked if the party leadership would seek a report on the matter, she said the party had got "absolutely nothing" to do with the case.
Any individual accused of any crime have to face the consequences and prove whether they are innocent or guilty, she said.
In Kerala, the state BJP demanded a comprehensive probe into the development.
"We want the Maharashtra police to conduct a comprehensive probe", BJP leader B Gopalakrishnan told reporters at Thrissur.