The fighting was sparked in the small town of Oakkan, around 100 kilometres north of Yangon, after a woman accidentally bumped into a young novice monk and knocked his alms bowl onto the ground, according to Ye Htut.
It is the latest unrest to flare in the region north of Yangon, Myanmar's main city, after a series of attacks by Buddhist mobs on Muslim homes, businesses and mosques in March.
He said some shops were destroyed but no buildings had been burnt.
"There were some attacks to the mosque by throwing with stones. No casualties were reported," a police official told AFP.
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At least 43 people were killed and thousands were left homeless in March in fighting apparently triggered by a quarrel between a Muslim gold shop owner and Buddhist customers in the central town of Meiktila.
The unrest has exposed deep religious tensions in the formerly junta-run nation and cast a shadow over reforms under a quasi-civilian regime that took power two years ago.
Last year around 200 people were killed in clashes between Buddhists and Muslim Rohingya -- a minority treated with hostility by many Burmese who see them as illegal Bangladeshi immigrants.
While the Rohingya -- described by the UN as among the most-persecuted minorities on the planet -- have long been denied Myanmar citizenship, the Muslims targeted in March's unrest are Myanmar nationals.
An official report into the unrest this week suggested doubling the security presence in the state and recommended keeping the communities apart as a temporary measure to prevent further violence.