The accused, identified as Nand Lal, had been arrested, they said.
The incident took place on Thursday evening when the victim went to her neighbour's house in the same building to take her mobile phone which she had put on charging there, police said.
"The accused took advantage of the situation and allegedly raped her and threatened her not to speak about the incident to anyone," said a police official.
The victim revealed her ordeal to her sister who informed the police.