It is the latest violence to hit Rakhine, which is festering with ethnic tensions and has been roiled by communal violence in the north against the Rohingya and insurgencies in other parts of the state.
Bombings in the state capital are rare however.
"Three bombs exploded and three other unexploded bombs were found. A police officer was injured but not seriously," a senior officer told AFP on condition of anonymity.
The blasts took place around 4:00am (2130 GMT Friday), the officer said.
One exploded in the compound of the state government secretary's home, while the two others hit in front of an office in the city and on a road leading to a beach.
A local official from the state government also confirmed the explosions.
The extent of the damage was not immediately clear.
"Some streets are being blocked by police already because of the bomb blasts," Zaw Zaw, a local resident of Sittwe, told AFP by phone.
In recent months unrest in Rakhine has been concentrated in the state's northern wedge, where a sweeping military crackdown on the Rohingya Muslim community last August pushed nearly 700,000 refugees across the border to Bangladesh.
The state capital Sittwe lies around 100 km south of the epicentre of that conflict.
The explosions come almost exactly six months to the day since northern Rakhine was plunged into crisis on August 25 when Rohingya rebels raided police posts, killing at least a dozen officials.
Myanmar's military responded with a ruthless campaign that the UN says amounts to ethnic cleansing of the Rohingya population, who are now overwhelmingly based in refugee camps in Bangladesh.
Myanmar authorities deny committing any atrocities but have blocked UN investigators from investigating the conflict zone, where thousands of Rohingya are believed to have been killed.
Sittwe was once home to a sizeable Rohingya population but most were forced to abandon their homes by deadly communal violence in 2012.
Today a small community of Rohingya are confined to a Muslim enclave in the city while more than 100,000 others are still living in squalid displacement camps outside the capital.
In a separate conflict in Rakhine state last month, seven people were killed and a dozen injured when police opened fire on a crowd of ethnic Rakhine Buddhists who were trying to seize a government office in the town of Mrauk U.
The violence prompted an ethnic Rakhine rebel group in the state to promise "serious" retaliation for the deaths of the protesters.
Around two weeks later the town's administrator was found murdered on the side of the road.
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