The girl's parents rushed her to hospital after discovering her bed covered in blood when they returned from work on Sunday. She later underwent a three-hour operation for her injuries.
The Press Trust of India said the girl's 27-year-old cousin had been arrested and charged under the Protection of Children from Sexual Offences Act, meaning he could face a life sentence.
Zainab's alleged murderer, rapist's previous criminal record comes to light
Swati Maliwal, the head of the Delhi Commission for Women, tweeted:
The worst has happened. An 8 month old baby has been brutally raped in the Capital and is battling for her life in a Hospital. Going to the hospital to meet her. Am totally numb. Terrified to face her! Please please pray for her.
— Swati Maliwal (@SwatiJaiHind) January 29, 2018
A UN Committee on the Rights of the Child in 2014 said one in three rape victims in India was a minor and expressed alarm over the widespread sexual abuse of children.
Nearly 11,000 cases of child rape were reported in India in 2015, according to the National Crime Records Bureau's latest figures.
It said three children were raped every day in Delhi alone.
The city, known as India's rape capital, hit global headlines in 2012 for the fatal gang-rape of a young female student.
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