Separate statements issued by their offices said they would not take part in any celebrations.
The governor and the chief minister also decided not to receive any New Year greetings in person.
"The usual exchange of greetings with members of the civil society has been cancelled at Raj Bhavan as homage to the death of the 23-year-old whose life was cut short by a heinous incident at Delhi," a statement from the Raj Bhavan said.
"In view of the sad demise of the Delhi girl following the unfortunate incident, Chief Minister N. Kiran Kumar Reddy personally decided not to take part in any New Year celebrations," said a statement from the chief minister's office.
Leader of Opposition and Telugu Desam Party (TDP) chief N. Chandrababu Naidu too declared he would not celebrate the New Year.
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Union Tourism Minister K. Chiranjeevi also made a similar announcement.
He participated in a candlelight vigil in Hyderabad Monday night to condole the death of the gang-rape victim.