The attack took place on a staircase in Bandra (East)'s Chetana college at 8.30 am on Saturday, where the victim and assailant were both third-year graduate students of a management studies course.
The man attacked the victim as she was walking back to class from a restroom with three of her female friends.
College peons and other students rushed to intervene when they heard her screams, and took them to the nearby hospital.
"The girl has suffered 8 to 10 stab wounds and is critical," said regional additional commissioner of police Vishwas Nangre Patil.
The victim had reportedly ended her friendship with the assailant because her parents were not comfortable with their closeness.
"We are investigating what provoked Bankar to take such a step," Patil said.