A new report by the charity, based on interviews with 65 "torture survivors", details systematic use of rape and beatings by prison guards.
Former detainees described so-called welcome parties - ritual beatings using metal bars and electric cables.
The Syrian government has repeatedly denied such allegations.
The report estimates that 17,723 people died in custody across Syria between March 2011, when the uprising against President Bashar Assad began, and December 2015 - equivalent to about 10 people each day or more than 300 a month.
According to the report, new detainees are subjected to "security checks" that often involve women being sexually assaulted by male guards.
"They treated us like animals. They wanted people to be as inhuman as possible," said Samer, a lawyer from Hama who was among those interviewed.
"I saw the blood, it was like a river... I never imagined humanity would reach such a low level."
Another inmate, Ziad (not his real name), described how seven people died in one day after the ventilation stopped working at an intelligence agency detention centre.
"They began to kick us to see who was alive and who wasn't," Ziad said.
Other detainees described being forced into a rubber tire or whipped on the soles of their feet. Amnesty says prisoners are routinely denied access to medical care and prevented from washing properly.
"For decades, Syrian government forces have used torture as a means to crush their opponents," said Philip Luther, Amnesty's Middle East and North Africa Director.
"Today, it is being carried out as part of a systematic and widespread attack directed against anyone suspected of opposing the government in the civilian population and amounts to crimes against humanity," he added.
A UN human rights report in February accused the Syrian government of carrying out a state policy of extermination, and said both sides in the war were suspected of committing war crimes.
Amnesty has called on the US and Russia, which co-chair peace talks on the Syrian crisis, to address the reports.
Talks have stalled however, with world powers failing in May to agree on a date for the process to resume. Talks in Geneva broke down in April after the opposition delegation quit, accusing the government of ignoring a ceasefire agreement.
More than 250,000 people have died in almost five years of war in Syria, with a further 11 million people displaced by the conflict, according to the UN.