Sri Lanka has declared a nationwide curfew for Tuesday, marking the second night of restrictions.
Several news outlets report that rioters killed a Muslim man as they torched shops believed to be owned by Islam adherents and vandalized mosques.
In at least six other towns police and the army used tear-gas to disperse rioters.
The attacks committed on this weekend of 11 May follow deadly attacks carried out on Easter Sunday of 21 April 2019, against churches and hotels in various parts of the country in which more than 200 people were killed and hundreds were injured.
Prime Minister Ranil Wickremesinghe has also urged calm, saying the current situation is hindering the investigation into the Easter attacks.
Sri Lankan police have arrested 23 people in connection with a spate of mob attacks on Muslim communities that left one person dead and dozens of shops and mosques destroyed.
One man died after being admitted to hospital with stab wounds, an officer at Marawila hospital said.
The curfew had been in place all day in North-Western Province (NWP), where police said a 45-year-old Muslim man was slaughtered in his carpentry shop late Monday by a crowd carrying swords.
Police said there were sporadic incidents of mobs throwing stones and torching shops, motorcycles and cars owned by Muslims.More news: Police officer shoots, kills Texas woman during arrest
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"The security forces have been given full powers to deal with those who violate the state of emergency and the islandwide curfew", he said.
Sri Lanka has a population of 21 million which is a patchwork of ethnicities and religions, dominated by the Sinhalese Buddhist majority. In the town of Kinyama, two mosques were smashed as outnumbered armed police and troops stood by.
A mosque official said the attacks were triggered when several people, including some Buddhist monks, demanded a search of the main building after soldiers had inspected a 43-hectare lake nearby.
Military spokesman Atapattu said security forces were arresting small groups of suspected trouble-makers and handing them over to police.
Internet service providers said they have been instructed by the telecoms regulator to block access to Facebook, WhatsApp, YouTube and Instagram in a bid to prevent the spread of messages inciting violence.
"Don't laugh more, 1 day u will cry", the shopkeeper wrote.
"Social media blocked again as a temporary measure to maintain peace in the country", Nalaka Kaluwewa, director general of the government information department, told Reuters on Monday.
The Lankan government also reimposed a ban on social media after the clashes.
Sri Lanka on Monday temporarily blocked some social media networks and messaging apps, including Facebook and WhatsApp, after attacks on mosques and Muslim-owned businesses in the worst unrest since Easter bombings by Islamist militants.