The woman is being treated at the All India Institute of Medical Sciences where her condition is stated to be critical.
The incident took place last night when the victim was alone at her house in Lajpat Nagar in south Delhi.
Police said Anil Kumar, 26, went to collect montly rent for the cable TV connection and when he found the woman alone he attempted to rape her.
A senior police official said Kumar allegedly inserted an iron rod inside the mouth of the victim when she cried for help.
As the woman shouted, neighbours came to her rescue and the accused escaped from the spot. However, he was later arrested.
Delhi was rocked by protests recently after the brutal gangrape and assault of a paramedical student in a moving bus.
She later died in a Singapore hospital.