Berkin Elvan, 15, spent 269 days in a coma before his death on Tuesday.
Many of the protesters echoed his mother’s claim that Turkish PM Recep Tayyip Erdogan was Berkin’s “killer”.
Police in the capital Ankara fired tear gas to disperse several thousand protesters who had gathered in the central Kizilay square.
Berkin Elvan was 14 when he was struck on the head by a tear gas canister while going to buy bread during last year’s unrest.
“Berkin’s murderers are the AKP police,” protesters shouted in Istanbul, referring to PM Recep Tayyip Erdogan’s ruling Justice and Development Party (AKP).
The crowds, shouting anti-government slogans, lit a huge fire as they made their way to a cemetery for the burial of the teenager.
“The rage of mothers will suffocate the killers,” screamed others.
Berkin Elvan’s death triggered violent protests in at least 32 towns and cities across the country on Tuesday – reminiscent of last year’s unrest.
President Abdullah Gul expressed his sadness and appealed for calm, urging everyone “to do everything to prevent this from happening again”.
He said Turkey was going through difficult days and that the “mind of the state has become overwhelmed by anger and hatred.”
The president added: “Little 15-year-old Berkin Elvan is the latest victim of this atmosphere.”
Correspondents say Berkin Elvan became a symbol of the heavy-handed tactics used by police to rein in the biggest demonstrations against the prime minister.
His death brought the toll from last year’s unrest to at least eight, including one policeman.
Berkin’s mother, Gulsum Elvan, had challenged Recep Tayyip Erdogan, who praised police “heroism” during the protests.
“It’s not God who took my son away but prime minister Erdogan,” the tearful mother told reporters on Tuesday.
The renewed unrest is likely to add to pressure on Recep Tayyip Erdogan, whose government has been rocked by an escalating corruption scandal ahead of elections that could decide his fate.
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