The actor was hanging for four minutes before fellow performers realised something was wrong.
Klimeck was taken to hospital suffering from cerebral hypoxia but died on Sunday.
The Passion play was being performed in Itarare, 345km (214 miles) west of Sao Paulo.
Klimeck was re-enacting the scene in which Judas commits suicide in repentance for his betrayal of Jesus Christ.
Police are investigating the apparatus that was meant to support Klimeck. It appears the knot may have been erroneously tied.
When the actors realised something was wrong, Klimeck was taken down and found to be unconscious.
The Santa Casa de Itapeva hospital has confirmed the death and an autopsy will take place on Monday.