According to a report by Human Rights Watch (HRW) published Friday, many were found in "overcrowded, filthy, bug- and vermin-infested cells."
The New York-based watchdog interviewed 42 children who were or have been detained, and made visits at several police stations and detention centres in Greece.
Under international and Greek law, minors can be detained only in exceptional conditions.
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Human Rights Watch, however, found that many were detained arbitrarily and for longer than the maximum allowed period of 45 days.
The report said, "Children face extremely poor conditions. In some cases, they were made to live and sleep in overcrowded, filthy, bug- and vermin-infested cells, sometimes without mattresses, and were deprived of appropriate sanitation, hygiene and privacy."
Meanwhile, Greece has asked Germany to pay reparations for the losses the Nazi war machine inflicted on the nation during World War Two.
The initiative is supported by Greek Prime Minister Alexis Tsipras and Greek non-attached MEP Sotirios Zarianopoulous.
Tsipras said, "We will pursue this to the end, first by diplomatic channels and if needed by legal channels."
His comments came during a ceremony held in memory of the 317 victims of the Kommeno village massacre, which occurred 73 years ago in northwest Greece.
Early in the morning of 16 August, 1943, the German army swarmed into Kommeno and executed 119 women, 97 babies and 101 men before setting the whole village on fire.
The Nazi troops committed a similar massacre in the Distomo village, in central Greece, on 10 June 1944, killing a total of 214 men, women and children.
In early December 1944, the Nazi soldiers also attacked Kalavryta town in southern Greece and massacred at least 700 people in the town and neighbouring villages in reprisal for Greek partisan attacks.
"Greece and the Greek people neither forget their history nor the Nazi war crimes and massacres," said Tsipras.
The Greek government has calculated the war reparations total €278.7bn at today's rates. Athens says the reparation amount includes a €10.3bn "occupation loan" that the Nazis forced Greece's Central Bank to pay during the war.
It is not the first time that Greece has demanded reparation from Germany. In April last year, Tsipras made a similar demand.
However, Germany strongly dismisses Athens' claims, saying it had already indemnified Greece in 1960 with a payment of 115 million Deutschmarks.
Although the sum was a fraction of the Greek demand at the time, Athens accepted the reparation with the agreement there would be no more claims, Berlin says.
Germany also says the issue of compensation was ultimately legally and politically settled in 1990 before Germany reunified.
Germany's minister for economic affairs and energy, Sigmar Gabriel, has described Athens' claims as "stupid."