Kayyum was arrested yesterday and has been charged with attempt of murder, Deputy Superintendent of Police Sanjiv Kumar Vajpayee said.
The woman had allegedly been raped a year back by the accused and she later filed a police complaint against him.
Kayyum resorted to shooting the victim after she refused to withdraw the case despite constant pressure from his side, police said.
The accused had been previously arrested on rape charges and was later released on bail.
The woman was shot at by Kayyum and two other bike-borne youths when she was alone at home in Janakpuri locality on Sunday.
The victim is in critical condition, police added.