Parliament wants answers about how Shepherd Bushiri and his wife managed to flee South Africa.
Home Affairs Minister Aaron Motsoaledi will appear before a portfolio committee on Tuesday to explain how they crossed the border without their passports.
eNCA reported that Shepherd Bushiri and his wife, Mary Bushiri planned their escape and snuck through the Beit Bridge Border post.
The couple allegedly paid officials at the border post.
The Hawks has issued an arrest warrant for the couple and the South African government has started an extradition process.