The man is not believed to have been a part of the demonstration.
The BBC reports the victim as 30-year-old Ugur Kurt.
Police used tear gas, water cannons and fired live bullets into the air to try to disperse a crowd angry at this month’s mining disaster, which killed 300.
The man was rushed to hospital after being hit by a bullet but medics were unable to save him.
"We have not been able to save Ugur Kurt," Istanbul governor Huseyin Avni Mutlu posted on Twitter, several hours after the victim was taken to hospital.
The trouble began when a group of about 12 began chanting slogans about another youth killed in a previous clash with police and the Soma mine disaster.
The group responded to the police’s tear gas by throwing rocks and petrol bombs.
The clash broke out in Okmeydani, a working-class district in central Istanbul.
CCTV footage shows Kurt collapsing in a pool of blood. He is believed to have been attending a funeral inside the complex of a cemevi, the house of worship for Turkey's Alevi religious minority, close to the ongoing riot.
About 400 demonstrators staged a sit-in outside the hospital, chanting: "Murderer state has taken another life."
Deputy Prime Minister Bulent Arincn told the BBC that prosecutors would investigate.
"If one of our citizens, who has nothing to do with the events, is injured by a stray bullet fired by a policeman, I would like to see anyone who is involved in this incident immediately be brought to account," Arinc said.