NEW DELHI — An 8-month-old infant girl has been hospitalized in India’s capital after being raped, the police said, a sexual assault that has both sickened and transfixed a city and country grown distressingly accustomed to horrifying sex abuse cases. A relative has been arrested.

As an indication of the widespread attention and concern the case has prompted, one major television station, NDTV, ran regular updates at the bottom of the screen on Tuesday:

“Baby in I.C.U.; Condition stable.”

According to police officials, the infant’s parents were working Sunday morning and had asked a cousin to watch their two girls, the 8-month-old and a 2-year-old. The family lives in a poor neighborhood in the northwest corner of New Delhi.

When the baby’s mother, a maid, returned in the afternoon, she found the infant bleeding profusely between her legs. Her father, speaking to television reporters with his face obscured to protect the family’s identity, said the bed the baby had been lying on had been smeared with blood.

The mother asked the cousin what had happened and he could not give her a clear answer.

She then called the police. After questioning, investigators arrested the cousin, a day laborer in his late 20s, who admitted to inserting his finger inside the infant girl’s vagina, police officials said.