The report by the European Committee for the Prevention of Torture and Inhuman or Degrading Treatment or Punishment (CPT) was sent to Greece in March but was made public only on Wednesday.
"There continues to be a widespread use of violence by the police against persons deprived of their liberty," it said.
A "considerable number" of people said they had been abused by police, mainly kicks, punches and blows with objects such as batons, it said. That was also the case in a 2001 visit, it said.
Greece said some allegations were not confirmed by its inquiries and said that it was working to improve conditions.
The report listed injuries observed on interviewees by the CPT's medical staff and said they were consistent with the abuse they said they suffered.
One man at Athens police headquarters, who said he was kicked, punched and beaten with a stick, had a swollen head, bruises on his face, back, legs and behind his knees.
Another man, who was held at the northeastern Soufli border guard station, said he was doused with cold water and forced to sit for about 13 hours overnight in front of an open window.
The committee found that detainees were often kept in overcrowded, unhygienic cells and not allowed enough exercise.
The report also highlighted the poor conditions in which immigrants are held, saying they were often detained in quarters with inadequate sanitary and other facilities.
"The delegation learnt that this man had been placed in a cage-like cell for several months," it said. The cell's area was only 3.5 square metres, it said.
In a written response to the report, Greece said some of the allegations were not borne out by its own investigations.
But it said Greece had "taken into consideration the findings and recommendations of the committee with the greatest seriousness and trusts that the measures that are being taken ... will improve the deficiencies of the prison system, the police stations and the detention facilities for aliens".