He is believed to be in detention in Tehran's notorious Evin Prison.
According to Amnesty, Makan told his family that if he signs a "confession" saying that the banned People's Mujahedin Organization of Iran (PMOI) killed her, then he may be released.
Amnesty says it fears he may be forced to sign such a "confession" under torture or other ill-treatment.
Makan was among those who witnessed Neda's horrific death on that street in Tehran on June 20.
Read the full Amnesty statement here.