They said the woman, Sudhir Bansal, was accompanying her son, Gaurav, who recently enrolled in Delhi University, to help him find accommodation.
They boarded the Yoga Express from Rajasthan. Ms Bansal was standing near the door of one of the compartments. When the train slowed down near Mithai Pul, on the way to the railway station, a thief caught hold of her bag, the police said.
The woman tried to fight him off but lost her balance and fell down on the tracks. She came under the wheels of the train and was injured, the police said.
Gaurav, her son, tried to save her from falling but was unsuccessful. She died while being taken to a hospital nearby. The thief fled with the bag containing cash, documents and an ATM card.
The woman's body was handed over her relatives after an autopsy, the police said.