Nazakkat Ali (19) was arrested following her complaint.
The girl was molested on Saturday night allegedly by a conductor when she had ran away from her house following harassment by her family.
The conductor Ranjit Singh was arrested in connection with the case, which comes close on the heels of the brutal gangrape of a girl in a moving bus in south Delhi.
Police went to her house in west Delhi's Khyala on Sunday to record her statement during which she told investigators about her ordeal.
A senior police official said her father had married thrice and they were living with his third wife. She claimed that there were problems in the family.
"She also told us that her brother had raped her six months ago and was molesting her thereafter. We have arrested the boy," the official said.
On Saturday night, the girl had left her house at around 9:30 pm and when the bus reached Mandi House at around 11pm, police personnel noticed the girl inside the bus alone crying.
A case of kidnapping was found registered about her at Khyala police station after her family approached police.