The 19-year-old was allegedly raped by four upper-caste men in Hathras district in northern India.
She was grievously injured and died in a Delhi hospital on Tuesday after fighting for her life for two weeks.
Activists say police must explain why they took the “inhumane decision”.
Her alleged attackers have been arrested and a fast-track court has been set up to hear the case.
Local journalist Abhishek Mathur, who witnessed the cremation from a distance, told the BBC that the police kept her family and media away from the funeral pyre.
Her body was brought to their village in Uttar Pradesh state around midnight. The victim’s brother said that police officials were putting pressure on the family to cremate her immediately.
“When we refused, they took the body in an ambulance and cremated her,” he said.
A senior district administration official, however, denied the allegation, saying the family’s consent was taken.
Mr Mathur said the victim’s mother wanted to take her body home for rituals before the last rites, but her request was denied.
“Police had formed a human-chain to stop the protesting crowds, the family and the media from getting close to the cremation spot,” he added.
The victim’s brother said some police officers were rude to them.
“They took the body away without our permission, without the permission of my parents and cremated her. We didn’t even get to see her one last time,” he said.
He further added that the police beat up members of the family when they protested to see the body, adding that even women members of the family were beaten up.