President Faustin Archange Touadera, re-elected in a disputed vote last month, announced the new measure in a statement on national radio.
He gave no information on the purpose of the curfew and it was unclear how the government intended to enforce it.
Touadera won five more years in power as a result of the December election. However, fighting has continued in towns nationwide since the election, with the rebels threatening to march on the capital, Bangui.
The political opposition insists Touadera’s victory lacks legitimacy. They have demanded a re-run.
Landlocked CAR is one of the world’s poorest nations and has seen a string of coups and wars since it gained independence from France in 1960.