The Delhi government has ordered a magisterial probe into the incident.
The child rights activist won the Nobel Peace Prize in 2014. He shared the prize with Pakistan's Malala Yousafzai.
The three accused brothers, Rajan alias Natta, 25, Vinod, 35, and Sunil, 28, have had previous involvements in burglary and robbery cases.
The Uber cab driver, who had allegedly raped a 27-year-old woman in Delhi on Friday night in his taxi, was planning to flee to Nepal before the police arrested him in the nick of time from Mathura in Uttar Pradesh.
A tussle between the Delhi government and the Lt Governor has left bureaucrats vulnerable to sudden transfers.