The government of the Buddhist-majority country has accused the monks of behaving like "animals" during Tuesday's attack on a centre housing Rohingya Muslims including children on the outskirts of Colombo.
"We have identified the monks who led the attack," an officer involved in the investigation told AFP on condition of anonymity.
"We have deployed three teams to arrest them."
Two police officers had to be hospitalised after the attack, in which monks and their supporters threw stones and smashed windows and furniture.
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The refugees had arrived in Sri Lanka five months ago after the navy found them drifting in a boat off the island's north coast.
Before that, they had been living in India for several years.
Hundreds of thousands of Rohingya Muslims have fled Myanmar in recent years and while most are in refugee camps in Bangladesh, a sizeable minority have moved to other parts of South Asia.
They have been the target of decades of state-backed persecution and discrimination in mainly Buddhist Myanmar, where many view them as illegal immigrants from Bangladesh.
The UN High Commissioner for Refugees expressed alarm over Tuesday's attack and urged Sri Lankans to show empathy for civilians fleeing persecution and violence.
The 31 Rohingya refugees, including 16 children and seven women, were evacuated by the police and accommodated at a former detention centre in the south of the island for their safety, according to the government.