He was shifted from a prison in Puzhal here to a prison in Vellore on Saturday, they said.
On May 23, Shaji, son of businessman here, allegedly drove a car in a rash and negligent manner under the influence of liquor and ran over three children sleeping on the pavement.
A 13-year old boy was killed and another was critically injured in the incident.
Shaji was arrested by Tamil Nadu police in Kochi on June 13 after absconding for about three weeks since the incident.