The boy had tried to throw a firebomb at a police patrol car.
Cars and shops burnt
Violence erupted as soon as news of Grigoropoulos's death in a local hospital had been confirmed.
Hundreds of youths in Exarchia began attacking police cars with stones and firebombs, burning dozens of cars and smashing shop windows.
Rioting quickly spread outside Athens to Thessaloniki and the holiday islands of Crete and Corfu.
Police responded by firing tear gas at the crowd, evacuating some restaurants in the area, and closing several streets to all traffic.
Emergency services tackled blazes in 16 banks, about 20 shops and more than a dozen cars in Athens alone.
As night fell, more than 1,000 students played a cat-and-mouse game with police in Athens, retreating to the university campus which security forces are forbidden to enter.
Barnaby Phillips, Al Jazeera's correspondent in the Greek capital, said local "people are shocked by the extent and ferocity of the violence".
|The riots will increase pressure on the already fragile Greek government [Reuters]
He said that the political fallout from the rioting would become clear in the coming days.
Costas Karamanlis, the Greek prime minister, expressed his sympathy in a letter to the parents of Grigoropoulos.
"In these difficult moments please accept my condolences for the unfair loss of your son," he wrote.
"Like all Greeks I am deeply saddened. I know that nothing can relieve your pain."
Karamanlis also said that those responsible would be brought to justice and that "the state will see to it that such a tragedy does not happen again."
In recent years, anger among Greek youths has been fanned by the growing gap between rich and poor.
Violence at student rallies and fire-bomb attacks by anarchist groups are common.
Plea for calm
Prokopis Pavlopoulos, Greece's interior minister, appealed for calm in wake of the rioting.
"Regarding the planned demonstrations, everyone has the right to protest but not by destroying property or turning against innocent people," he said.
Pavlopoulos denounced the violence as "against human rights" and defended the police response, saying that "no rage, even justified, must lead to protests like those we saw [on Saturday]".
He said he had offered his resignation but it had been rejected by Karamanlis.
Karamanlis's government has lost three ministers to scandals in the last 12 months alone.