The girl is reportedly in a critical condition at a local hospital where she was brought in on Sunday.
Police told the media that they had arrested the 28-year-old accused, described as a daily wage worker.
Delhi Commission for Women chief Swati Maliwal, who visited the infant in hospital on Monday night, described her injuries as "horrific".
The incident happened on Sunday but came to light on Monday after local media reported it.
Ms Maliwal tweeted that the girl had to undergo a three-hour operation.
"Her heart-rending cries could be heard in the intensive-care unit of the hospital. She has horrific injuries in her internal organs," she tweeted.
She posted another tweet expressing her anguish.
"What to do? How can Delhi sleep today when 8 month baby has been brutally raped in capital? Have we become so insensitive or we have simply accepted this as our fate?" she tweeted.
Ms Maliwal also posted a direct appeal to Prime Minister Narendra Modi that "stricter laws and more police resources" were needed to protect girls in the country.
Scrutiny of sexual violence has grown in India since the 2012 gang rape and murder of a 23-year-old student on a bus in the capital Delhi.
The crime sparked days of protests and forced the government to introduce tougher anti-rape laws, including the death penalty.
However, brutal sexual attacks against women and children continue to be reported across the country.