Sister Gertrud Tiefenbacher was found murdered in her room at the Sacred Heart Home Convent in the village of Ixopo, southwest of Durban, almost two weeks ago.
Detectives said three men, aged between 25 and 35, had been detained and they would appear in court on Wednesday.
In a statement officers said: "They were found in possession of some of the stolen property which were positively identified as property belonging to the victim.
"It is alleged that foreign currency had been taken from Tiefebacher's room. It is also suspected that the victim was raped before she was killed."
Sister Gertrud had worked as a school secretary and administration officer at the convent for 40 years.