The group says it believes all of those who died were arrested after taking part in anti-government protests.
Foreign journalists have been blocked from entering Syria and the reports could not immediately be verified.
The allegations, published in a report, come shortly after the Syrian government denied persistent reports of at least one mass grave being uncovered in the restive southern city of Deraa.
"These deaths behind bars are reaching massive proportions, and appear to be an extension of the same brutal disdain for life that we are seeing daily on the streets of Syria," said Neil Sammonds, Amnesty's researcher on Syria.
Mr Sammonds told the BBC that they have the names of at least 3,000 people who are currently in detention.
"There are said to be 12-15,000 people detained in the country at the moment. We know that torture has been widespread over many years and it has got much much worse. Most people are held in incommunicado detention."
He said the volume of abuses, many of which had been documented on video and occurred near the cities of Homs and Deraa, had returned almost to levels not seen since the 1980s.
Deraa was the first Syrian city to see pro-democracy protests, in mid-March, and became an epicentre of the unrest after security forces launched a major operation to crush any dissent there. Dozens of people are believed to have been killed and hundreds arrested.
In its report, Amnesty said that the victims were all men or boys and, in at least 52 of the cases, there was evidence that torture or ill-treatment caused or contributed to the deaths.
Deaths in detention have also been reported in five other governorates - Damascus and Rif Damashq, Idlib, Hama and Aleppo, Amnesty said.
Amnesty International says it has compiled the names of more than 1,800 people reported to have died since pro-reform protests began. Thousands of others have been arrested, with many held incommunicado at unknown locations, according to the group.
Residents said that in the early hours of Wednesday morning Syrian troops backed by tanks raided houses looking for activists in two main districts of Hama.
A local activist told Reuters that several tanks were parked at a bridge at the eastern entrance to the city and then hundreds of troops entered two neighbourhoods on foot.
On Tuesday, as people streamed out of mosques after prayers to mark the end of Ramadan and renewed protests against Syrian President Bashar al-Assad, security forces shot dead four demonstrators.
Those who died, including a 13-year-old boy, were killed in the towns of al-Hara and Inkhil in the southern province of Deraa.