40-year old Reddy was getting into his car after visiting a lab run by him here last night when the assailants attacked him with sharp weapons killing him on the spot, they said.
Reddy was also into social service and had been offering free treatment to poor people in hospitals run by him in the city.
Police said they were investigating the motive behind the murder, which sent shock waves among the medical fraternity and his supporters.
The state chapter of Indian Medical Association expressed shock over the killing of Reddy and said incidents of attacks on medical professionals in the state had been on the rise.
IMA state Secretary Dr J A Jayalal in a statement in Chennai urged chief minister Jayalalithaa to take recourse to all steps to eradicate the "growing culture of violence".
He said hospitals in Vellore District would remain closed today protesting the murder. IMA members would stage a fast in Chennai if necessary action to ensure protection of doctors and hospitals was not taken within a week, he said.