The curfew, which will run from 6:00 pm to 6:00 am, was announced by the Abia state governor late on Tuesday, who told residents to remain at home and avoid any form of confrontation with the security forces or military.
It will be in force until Friday.
Recent days have seen clashes between supporters of the Indigenous People of Biafra (IPOB), which want independence for the dominant Igbo ethnic group, and the military.
On Sunday, IPOB claimed five of its members were killed but the army described the claims as "fictitious" and "far from the truth".
IPOB leader Nnamdi Kanu has been charged with treasonable felony and is currently on bail pending the resumption of his trial in the capital, Abuja, next month.
Tensions have risen since he was freed from custody in April, with the government accusing him of breaching his bail conditions.
Abia governor Okezie Ikpeazu suggested the presence of soldiers, who began operations against kidnapping and violent crime across southern Nigeria this week, may be at the root of tensions.
He attributed Sunday's clashes to the start of the crackdown on crime, which is codenamed "Python Dance II".
On Wednesday, IPOB said troops had taken over Kanu's home in Abia state capital, Umuahia, and that four of his supporters had been killed as they tried to stop them.
The group's welfare office, Ikechukwu Ugwoha, told AFP "around 50 to 60" others were missing.
Another separatist group, the Movement for Actualisation of the Sovereign State of Biafra (MASSOB), called for the military to withdraw.
"What is happening in the southeast is totally uncalled for," group leader Madu Uchenna told AFP.
A previous unilateral declaration of an independent republic of Biafra in 1967 led to a brutal 30-month civil war that left more than one million dead, most of them Igbos.