The Sri Lankan government has imposed an indefinite curfew in the North Western Province of the country, where a Muslim man was killed by a mob on Monday, police said, in a violent backlash against last month's bombings.

The 45-year-old died of injuries sustained when a crowd stormed his carpentry workshop in the Puttalam district in the NWP and slashed him, official sources said.

Police chief Chandana Wickramaratne warned of stern action against rioters, and said that constables have been issued orders to use "maximum force".

Elsewhere in the province, mobs torched dozens of Muslim-owned shops, vandalised homes and mosques in a day of rioting.

"The curfew in the NWP will be continued until further notice," police spokesman Ruwan Gunasekera said.

Sri Lanka also temporarily banned some social media networks and messaging apps, including Facebook and WhatsApp, after a posting sparked anti-Muslim riots across several towns.