A Juhu police station official said the actress (66) and the accused (38) are known to each other, but are not on talking terms of late following some dispute.
He said the accused, also a resident of upscale Juhu, kept calling the actress and even used to stalk her even after she had asked him against doing so.
The actress approached the police yesterday and lodged a complaint.
Police have registered an FIR under sections 354 D (stalking), 509 (word, gesture or act intended to insult the modesty of a woman) and other relevant sections of the IPC against the businessman, the official said.