In a report titled "Libya is full of cruelty", the rights group collected the testimonies of 90 migrants, including 15 women, interviewed in reception centres in Italy and Sicily after escaping Libya in recent months.
Amnesty said that sexual abuse is so widespread that some women take contraceptives before their sea crossing.
It cited a 21-year-old Eritrean woman identified as Amal who said she was among a group of 11 Christian women from Eritrea who were abducted by IS militants in July 2015.
They were kept in underground detention for nine months, forced to convert to Islam and used as sex slaves.
In other instances migrants were shot or electrocuted and in one case a disabled migrant was dumped in the desert by people smugglers.
Libya is home to some 250,000 refugees and migrants.
The UN refugee agency estimates that since April 19 2015, a total of 4,937 people have died trying to cross the Mediterranean from Libya to Europe.
Magdelena Mughrabi, from Amnesty, said: "From being abducted, incarcerated underground for months and sexually abused by members of armed groups, to being beaten, exploited or shot at by people smugglers, traffickers or criminal gangs - refugees and migrants have described in harrowing detail the horrors they were forced to endure in Libya,"
She also urged the international community to take action to tackle the root causes of migration and to increase the number of people who are resettled overseas or given humanitarian visas.