The attack on line 7 of the metro on Thursday evening prompted a fellow passenger, Rajinder Singh, to intervene to help the woman. He became involved in a struggle with the mugger, which spilled off the train and onto the platform. Mr Singh died when he was pushed or fell onto the train tracks and was electrocuted.
The woman, described as young and blonde, has not yet come forward. She will be able to provide important evidence to police as part of their inquiry.
Police arrested a 22-year-old Egyptian man on Tuesday in connection with the incident after identifying him from video surveillance footage. He was picked up by police in a bar in the Pigalle area of the city on Tuesday evening after receiving a call from someone who had seen the suspect.
Two government ministers visited the Crimée metro station on Wednesday to pay their respects to Mr Singh, known to his family and friends as Babu, who had moved to Paris seven years ago from his native Punjab in India.
Transport minister Thierry Marani and culture minister Frédéric Mitterrand laid a wreath at the makeshift shrine in the station.
"He was a hero," said Mariani. "He came to France, didn't cause any trouble, worked, sent money to his family and was respectful of certain values. I find it very moving."
Mariani also confirmed that the costs of sending Mr Singh's body home to India would be covered by the Paris transport authority RATP.
Frédéric Mitterrand paid his respects to "poor Babu who was one of the everyday heros who make life better" and who "represented everything that is wonderful about the Indian culture, the sharing and the caring for others."