Two out of three of the 12,446 respondents between the ages of five and 18 reported having been physically abused.
This included slapping, kicking or beating with a stick, and in most cases the abuse had been initiated by parents or teachers.
More than 50 per cent said that they had been sexually abused.
The study also interviewed 2,324 young adults between the ages of 18 and 24, almost half of whom reported being physically or sexually abused as children.
In almost 80 per cent of the cases the abuser was a person well known by the child.
Chowdhury said that a culture where children were taught to obey adults unconditionally and where there was a strong taboo on talking openly about sex contributed to the problem.
She said: "Quite often they end up being silent victims."
In 70 per cent of the cases of sexual abuse, the child did not tell anyone what had happened.
The study was conducted in 13 states by Prayas, an Indian non-governmental group, and backed by Unicef, the United Nation's child welfare agency, and the Save the Children Fund.
Children, chosen at random, were questioned on the street, at work, in schools, in institutions and in their own homes.
Child rights activists welcomed the study, saying it was positive that the government was waking up to the reality of abuse in India.
Kailash Sathyarthi of Bachpan Bachao Andolan, the Indian Save the Childhood movement, said: "Homes, schools and neighbourhoods are not safe for our children as most people don't even believe that hitting or sexually abusing a child is a serious crime.
"Laws need to be strengthened and mindsets need to be changed if we are serious about protecting our children."
Of India's 1.1 billion population, more than a third are aged under 18.
The study was released three months after police discovered the bodies of 19 people, mainly children, in a drainage ditch in a New Delhi suburb.
The children were suspected to have been abducted from a nearby village over several years.
Indian police have charged a domestic worker, Surinder Koli, with the rape and murder of the victims.
In March, India's parliament called for new laws to protect children in the wake of the slaughter, which was termed a "national shame".