Three bombs have exploded in Sittwe, the capital of Myanmar's restive Rakhine province, police say.
A police officer was slightly injured in the blasts. It was unclear who was behind them, police said.
One of the bombs went off near the home of a local official.The others went off near a court and a record office.
More than half a million mainly Muslim Rohingya from Rakhine fled the destruction of their homes last year in what the UN called ethnic cleansing.
Villages where Rohingya had lived were burned and several thousand people were killed in retaliation after Rohingya militants staged a series of attacks on police outposts.
The military in Myanmar (Burma) says it is fighting militants and denies targeting civilians.
There has also been tension between the authorities and ethnic Rakhine Buddhists after seven people were killed last month when police opened fire on a crowd trying to seize a local government office.
An ethnic Rakhine rebel group in the state vowed retaliation for the deaths of the protesters, AFP news agency reports.
Police spokesman Colonel Myo Thu Soe told Reuters news agency three other unexploded hand-made bombs had been found in the city.
Sittwe is about 100km (60 miles) south of where most of the violence against Rohingya has taken place.
Most of Sittwe's Rohingya population left their homes after religious violence in 2012. More than 100,000 people are still living in internment camps outside the city.
Separately, satellite images suggest entire Rohingya villages, many already damaged by fire, have been completely bulldozed, campaign group Human Rights Group says.
It said the apparent destruction of homes erases evidence for legal claims from the exiled Rohingya.