The polls were initially to have been held on October 18 but were postponed, in part due to violence in the capital.
A run-off presidential vote will be held on January 24 if needed, state radio said.
The elections are intended to usher in a government with authority to restore order in one of Africa's most turbulent states and pave the way for the departure of UN and French peacekeepers.
Central African Republic was plunged into turmoil in 2013 when Muslim rebels from an umbrella group called Seleka seized power in the majority-Christian country.
Seleka handed power to a transitional government in 2014 under international pressure but months of violence followed, killing thousands and resulting in the effective partition of the country.
The murder of a Muslim man in the capital in late September triggered inter-communal violence that killed at least 40 people, forced 40,000 to flee and destroyed homes, shops and humanitarian offices.
In August a transitional council adopted a new constitution, which will be put to a referendum one week before the elections, the radio said. All the main political groups say they support it so it is likely to be adopted.