The woman was on her way to college when she was allegedly dragged into a van at Charkop in a Mumbai suburb. She has told the police that she was assaulted as the vehicle was driven to Madh Island near Mumbai and later thrown out.
"We have registered a case and are investigating," said senior police officer Vikram Deshmane.
The woman has given the vehicle's registration number, which is being tracked down by the police.
The police are trying to retrieve CCTV footage from the area where she was allegedly kidnapped.
The government brought in tougher laws on rape after angry street protests engulfed India over the brutal gang-rape in Delhi of a young medical student in December 2012. The 23-year-old was raped and tortured on a moving bus before being thrown onto the road. She died 16 days later.