The incident happened on May 20 but it came to light yesterday after a man rang up the Delhi Commission For Women (DCW) helpline.
The minor girl has been admitted to Aruna Asaf Ali Hospital, where she is undergoing treatment for an infection in her private parts, police said.
According to the police, 30-year-old Shiva lured the victim on the pretext of giving her sweets and sexually assaulted her.
The girl was in pain but her mother could not understand what she was going through. Meanwhile, a man somehow learnt about the incident and informed the Commission, they said.
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The victim lives with her mother beneath a flyover in the city. Her mother, who works as a rag picker, has been homeless for the last six years, police added.
DCW chief Swati Maliwal visited the girl at the hospital this evening.
"Shameful. 6 year old homeless girl brutally raped in Delhi. Accused 30 years of age and is arrested. Going to hospital to meet her," she tweeted.