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Governor Nasir Ahmad el-Rufai also said anyone who is convicted of raping a child under the age of 14 will be given the death penalty under the new legislation.
Nasir Ahmad el-Rufai said the "drastic penalties are required to help further protect children from a serious crime".
The move comes after public outrage following a recent increase of rape charges amid the country's Covid-19 restrictions.
The new castration laws come after women's groups called for tougher action against rapists, including the death penalty.
Kaduna state's new law is the strictest against rape in Nigeria, Africa's most populous country.
Rapists will also face life imprisonment. Previous laws carried a maximum penalty of 21 years' jail for the rape of an adult and life in jail for the rape of a minor.