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.