The report, issued on Tuesday, said that 20-50 people were hanged each week, sometimes twice a week, at the Saydnaya prison in what the organization called a "calculated campaign of extrajudicial execution."
The report covers the period from the start of the March 2011 uprising to December 2015, when Amnesty says between 5,000 and 13,000 people were hanged.
Lynn Maalouf, deputy director for research at Amnesty's regional office in Beirut, said there is no reason to believe the practice has stopped since then, with thousands more probably killed.
Amnesty said the killings were authorized by senior Syrian officials, including deputies of President Bashar Assad.
"The horrors depicted in this report reveal a hidden, monstrous campaign, authorized at the highest levels of the Syrian government, aimed at crushing any form of dissent within the Syrian population," Maalouf said.
"These executions take place after a sham trial that lasts over a minute or two minutes, but they are authorized by the highest levels of authority," including the Grand Mufti, a top religious authority in Syria, and the defense minister.
There was no immediate comment from the Syrian government on Tuesday, and Amnesty said Damascus didn't respond to its own letter seeking comment. Syrian government officials rarely comment on allegations of torture and mass killings. In the past, they have denied reports of massacres documented by international human rights groups, describing them as propaganda.
The Amnesty report prompted a strong reaction from United Nations Secretary-General Antonio Guterres, who, "was horrified about what was in the report," according to UN spokesman Stephane Dujarric.
"We have repeatedly raised serious concerns about the grave violations of international human rights and international humanitarian law in Syria, including in detention centers and government-run prisons," Dujarric told reporters at UN headquarters in New York. "What is important is that there needs to be accountability for all the victims in this conflict."
Amnesty had recorded at least 35 different methods of torture in Syria since the late 1980s, practices that only increased since 2011, Maalouf said.
Other rights groups have found evidence of widespread torture leading to death in Syrian detention facilities. In a report last year, Amnesty found that more than 17,000 people have died of torture and ill-treatment in custody across Syria since 2011, an average rate of more than 300 a month.
Those figures are comparable to battlefield deaths in Aleppo, one of the fiercest war zones in Syria, where 21,000 were killed across the province since 2011.
Saydnaya has become the main political prison in Syria since 2011, according to a former official interviewed by Amnesty. A former guard said it held "the detainees of the revolution," and a former judge said they were seen as "posing a real risk to the regime."
The chilling accounts in Tuesday's report came from interviews with 31 former detainees and over 50 other officials and experts, including former guards and judges.
Detainees were told they would be transferred to civilian detention centers but were taken instead to another building in the facility and hanged.
"They walked in the 'train,' so they had their heads down and were trying to catch the shirt of the person in front of them. The first time I saw them, I was horrified. They were being taken to the slaughterhouse," Hamid, a former detainee, told Amnesty.
Another former detainee, Omar Alshogre, told The Associated Press the guards would come to his cell, sometimes three times a week, and call out detainees by name.
Alshogre, 21, who spent nine months in Saydnaya and now lives in Sweden, said he would hear detainees being tortured. "Then the sound would stop," he said.
He described how at times he was forced to keep his eyes closed and his back to the guards while they abused or suffocated a cellmate. The body often would be left behind, or there would be a pool of blood in the cell for other prisoners to clean up.
The Amnesty report contains similar accounts of abuse.
"We already know they will die anyway, so we do whatever we want with them," Amnesty quoted a former guard as saying.
The detainees were transported to trials in vans known as "meat fridges," and would not be informed of their fate until just before they were hanged, officials who witnessed the executions told Amnesty.
Medics would usually list the cause of death as "heart stopped," or "breathing stopped," before the bodies were taken to mass graves near Damascus.
Alshogre, who was arrested at the age of 17, spent time in several detention centers before being taken to Saydnaya.
Two cousins detained with him in western Syria didn't survive, dying a year apart in a military intelligence detention facility. The younger one died in Alshogre's arms, deprived of food and so weak he was unable to walk to the bathroom on his own.
Still, Alshogre said nothing could have prepared him for Saydnaya.
At one point, he was summoned by guards "for execution," he said. He was brought before a military tribunal and told not to raise his eyes to the judge, who asked him how many soldiers he had killed. When he said none, the judge spared him.
Alshogre survived nine months in Saydnaya before eventually paying his way out in 2015 — a common practice. He suffered from tuberculosis and his weight fell to 35 kilograms (77 pounds).
Death in Saydnaya was always present, "like the air," he said.
Once when he was deprived of food for two days, a cellmate handed him his food ration — and died days later. Another cellmate died of diarrhea, also common in the prison.
"Death is the simplest thing. It was the most hoped for because it would have spared us a lot: hunger, thirst, fear, pain, cold, thinking," he said. "Thinking was so hard. It could also kill."