Unsubstantiated rumors of unrest in other parts of the country such as Yangon are spreading via text messages and social media, stoking fears among residents.
"People are feeling totally insecure, totally not safe," said Aye Chan Naing, the founder of Democratic Voice of Burma, an independent news website based in Chiang Mai, Thailand, less than 200 kilometers from the border with Myanmar.
In one example, Si Thu, a Buddhist employee of the United Nations who lives in a mainly Muslim neighborhood of Yangon, said Tuesday he was moving his family to stay at a relative's home elsewhere in the city.
"I can't think of any political or religious aspects now," he said. "I only know about how to protect my family."
The New Light of Myanmar suggested that such rumors are being "circulated by those with ill will who want to harm peace and stability."
The clashes in Meiktila and elsewhere have drawn expressions of concern from U.N. and U.S. officials.
The sudden boiling over of tensions between Buddhists and Muslims in central Myanmar follows sectarian troubles that killed scores of people in the west of the country last year.
Those clashes, in Rakhine state, took place between the Buddhist majority and the Rohingya, a stateless ethnic Muslim group.
Most of the victims in that unrest were Rohingya. Tens of thousands more were left living in makeshift camps, and many of them have since joined those who attempt each year to flee to Thailand and Malaysia in flimsy boats.