All three men were students at Aleppo University - Basel Aslan and Musab Barad were fourth-year medical students and Hazem Batikh was a second-year English literature student and a first-aid medic, said the London-based rights group.
"The discovery of the charred and mutilated bodies of three young medical workers a week after their arrest in Aleppo city is yet further evidence of the Syrian government forces' appalling disregard for the sanctity of the role of medical workers," it said.
The three "were part of a team of doctors, nurses and first-aiders who have been providing life-saving medical treatment in makeshift 'field hospitals' set up to treat demonstrators shot by security forces".
They could not therefore go to state-run hospitals for fear of being arrested, tortured or even killed, it said.
The three medics had been detained by Air Force Intelligence since their arrest in the city on June 17.
"The brutal killing of these young medics who took great personal risk to rescue and treat injured protesters is yet more evidence that Syrian government forces are prepared to commit unspeakable crimes to silence dissent," said Donatella Rovera, Amnesty International's senior crisis response adviser.
Ms Rovera recently returned from several weeks in Syria.
"As casualties from the current unrest have mounted, so President Bashar al-Assad's government has intensified its hunt for the wounded and for those who provide life-saving emergency treatment to them," she added.
"Such violations are part of an increasingly entrenched pattern of crimes against humanity being perpetrated with impunity by Syrian government forces."
Amnesty said the three students' burned bodies were found in the early hours of Sunday in a burned-out car in the Neirab area of Aleppo's northeastern outskirts.
Medical personnel who saw the bodies at the morgue told Amnesty International that Aslan had a gunshot wound to the head and his hands were tied behind his back.
One leg and one arm were broken, several teeth missing and the flesh was missing from his lower legs, leaving the bone exposed. Some of his fingernails had been removed.
The bodies of the others were more heavily burned and also bore other wounds.
Amnesty International has seen images of the corpses that back up these descriptions.
The students' identity cards and university cards were found intact alongside their bodies, indicating that they had been left there after the bodies were burned.
A fourth, charred corpse found with the men has yet to be identified.
Shortly after the three students were arrested, one of their parents called their son's mobile phone and an unidentified man reportedly answered, saying: "You don't know how to raise your son. We will teach him how to behave", said Amnesty.
