Mya Thwe Thwe Khaing was injured last week when police tried to disperse protesters using water cannon, rubber bullets and live rounds.
Her wound was consistent with one from live ammunition, rights groups said.
Myanmar has seen days of protests following a coup which overthrew Aung San Suu Kyi’s elected government.
The hospital in the capital Nay Pyi Taw confirmed her death at 11:00 local time (04:30 GMT). A funeral service will be held on Sunday, her family said.
“We will look for justice and move forward,” a doctor told AFP news agency, adding that staff had faced immense pressure since she was taken to their intensive care unit.
Authorities said they would investigate the case.
Mya Thwe Thwe Khaing, who turned 20 after she was shot, had been on life support since she was taken to hospital on 9 February.
She had taken part in a protest in the south-east Asian nation which saw police use water cannon against protesters who refused to retreat.
According to BBC Burmese, who spoke to an unnamed medical officer shortly after she was brought to the hospital, she suffered a serious head injury.
Mya Thwe Thwe Khaing’s family are all supporters of Ms Suu Kyi’s National League for Democracy (NLD). Her brother said she voted for the first time in last November’s general election, which the NLD won by a landslide.
“I want to encourage all the citizens to join the protests until we can get rid of this system,” her sister, Mya Tha Toe Nwe, told reporters shortly after the death was announced on Friday. “That’s all I want to say.”
With inputs by BBC.