The simultaneous blasts occurred at two crowded shopping malls and a trade centre in Yangon, government officials said; but they gave no further details.
"Nine people were killed and several dozen more were admitted with blast wounds," an official at Yangon General Hospital told Reuters.
One blast killed up to three people and wounded over 10 others attending a Thai trade fair at the Yangon trade centre, a Thai Foreign Ministry official said in Bangkok.
Witnesses said traffic was jammed outside the shopping centres as rescue teams worked to evacuate the wounded. Other shopping centres in the capital were closed after the blasts.
Series of blasts
It was the latest in a series of explosions in the former Burma, ruled by the military in various guises since 1962.
Last month, a bomb blast at a busy market in the central city of Mandalay, 690km north of Yangon, killed 3 people and wounded another 15.
The military has blamed previous attacks on "destructive elements" - an expression often used to refer to political opponents and ethnic minority rebel groups fighting for autonomy.
A spokesman for the Karen National Union, a rebel group based along the Thai-Myanmar border, said on Saturday his group was not responsible for the blasts.