The curfew in the North-Western province will remain until further notice, police said.
Mosques and Muslim-owned shops have been vandalised or set on fire, and one Muslim man has been slashed to death.
In several towns, police fired into the air and used tear gas to disperse mobs.
Tensions have been high since Islamist militants attacked churches and hotels on Easter Sunday, killing more than 250 people.
In a televised address, Police Chief Chandana Wickramaratne warned that officers would respond to rioters with maximum force.
Prime Minister Ranil Wickremesinghe also appealed for calm in the early hours of Monday, saying the current unrest was hampering the investigation into last month’s attacks.
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