Mya Thwate Thwate Khaing, who just turned 20, had been on life support since being taken to hospital on 9 February, after she was hit by a bullet at a demonstration in the capital, Naypyitaw.
Video on social media shows her sheltering from water cannon with her sister behind a bus stop in the moments before the shooting.
A crack can be heard before she is seen falling to the ground.
Myanmar's military seized power in a coup on 1 February, forcing elected leader Aung San Suu Kyi into detention.
The ruling junta has cut internet connections, imposed a curfew and a law banning more than five people from congregating in an effort to stop the demonstrations that have sprung up since their takeover.
Some members of the security forces have already used violence against the protesters - driving tanks into major cities and opening fire on the crowds.
Almost 400 people have been detained since the coup.
On the day of Mya's shooting, photographs show at least one officer at the protest was armed with a submachine gun, although there is no confirmation the bullet that hit Mya was from his gun.
The military said in a statement: "As the protesters did aggressive acts against police members at about 12.30pm, the police members had to shoot inevitably."
Mya's brother, Ye Htut Aung, said he felt "really sad".
Mya was the first known serious casualty of the protests and her wounding rallied support for the movement seeking to reverse the coup - and free Ms Suu Kyi and her allies from detention.
Youth leader Esther Ze Naw said: "We cannot stay quiet. If there is blood shed during our peaceful protests, then there will be more if we let them take over the country."