The allegations are made in an 18-page report released Thursday by the international rights group.
The report details testimony from former detainees of the facilities run by the Islamic State in Iraq and al-Sham, known as ISIS.
Their testimony described flogging with rubber generator belts and torture with electric shocks. Some prisoners had their wrists secured together over one shoulder.
Detainees held by ISIS "include children as young as 8 who are held together with adults in the same cruel and inhuman conditions," said Philip Luther, AI's director for the Middle East and North Africa.
Some of the detained children were flogged as their parents were forced to listen to their screams in a nearby room, Amnesty said. Two detainees said a child about 14 years old received more than 90 lashes. A child accused of stealing a motorbike was repeatedly flogged for several days.
Amnesty International said it had identified seven secret prisons run by the group in northern Syria, primarily in Aleppo and the al-Raqqa governorate.
Amnesty called on ISIS to end its inhumane treatment of detainees and for its leaders to tell members to respect human rights and abide by international law. It also called on the international community to block the flow of arms to the organization.
"The Turkish government, in particular, should prevent its territory being used by ISIS to bring in arms and recruits to Syria," Luther said.