The security forces clamped the indefinite curfew ahead of demonstrations called by residents to protest Thursday's killing of seven men the army described as Tiger suspects.
The rebels regard those killed as civilians.
The authorities also announced the main entry and exit point to rebel-held territory in Jaffna will be shut on Monday, a military official said.
The latest moves came as eight more people were reported missing in Jaffna.
The men had slept overnight at a Hindu temple after a ceremony in the peninsula before troops allegedly took them away, the rebel Liberation Tigers of Tamil Eelam (LTTE) said in a statement.
They said villagers found blood and three identity cards belonging to the missing men.
The defence ministry said it had no information about the Tiger allegations but said that in the country's east, troops and Tamil Tiger rebels traded mortar and automatic rifle fire on Sunday.
"There are no casualties among troops but we don't know if there are any on the