Local media write about dead protesters in at least three cities: Yangon, Mandalay and Sagaing.
Several people are also said to have been injured during the protests that took place while the army was celebrating the officially proclaimed "armed forces day", writes Reuters.
On state television, protesters are being warned that they could be shot in the head or back.
The violence comes the day after one of the leaders of Myanmar's military dictatorship, General Min Aung Hlaing, said he defended democracy and would hold general elections, without giving any time frame for when it would happen.
The military occupation of Myanmar started in February and has caused several fatal protests.