Khin Myo Chit's family told the BBC he was killed by police as they ran to his father, during a raid on their home in Mandalay.
Myanmar's military has continued to increase its use of force as protests continue.
The rights group Save the Children says more than 20 children have been killed.
In total, the military says 164 people have been killed in protests, and the Assistance Association for Political Prisoners (AAPP) has killed at least 261 people.
The soldiers on Tuesday expressed their grief over the deaths of the protesters, while accusing them of causing unrest and violence in the country.
But security forces used rounds to protest the protesters, and there were numerous reports of people being beaten and sometimes shot as soldiers stormed houses to arrest activists and protesters.
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'Then they shot him'
Khin Myo Chit's older sister told BBC police they searched all the homes in her area of Mandalay on Tuesday afternoon, when they finally entered their area to search for weapons and arrest.
"They kicked the door open," said 25-year-old May Thu Sumaya. "When the door opened, they asked my father if there were any other people in the house."
When he said no, they accused him of lying and started searching the house, he said.
This was the time when Khin Myo Chit ran to his father and sat on his lap.
"Then they shot and beat him," said May Thu Sumaya.
In an exclusive interview with Myanmar Muslim Media, their father U Maung Ko Hashin Bai explained the last words of his child. "He said, 'I can't, Dad, it's too painful.'
He said he died just half an hour later when he was rushed to a car for medical attention. Police also beat and arrested his 19-year-old son.
The military has yet to comment on the deaths.
In a statement, Save the Children said the girl's death was "very shocking", and a day later it was reported that a 14-year-old boy had been shot dead in Mandalay.
"The deaths of these children are about reports that they were killed at home, where they should have been safe. The fact that so many children are being killed almost every day now shows a complete disregard for the safety of the people," the group said.
Meanwhile on Wednesday, authorities released about 600 inmates from Insein Prison in Yangon (Rangoon), most of them university students.
Associated Press journalist Thein Zaw was one of the released. He and other journalists were arrested for reporting on protests last month.
The AAPP says at least 2,000 people have been arrested in the campaign so far.
The protesters have called for a general strike and for more businesses to be closed and for people to remain at home. There are also plans for overnight candlelight vigils, in Yangon and elsewhere.