Burger, the powerful loose-forward, and centre Fourie are both out of action with knee ligament damage while scrum-half Du Preez is recovering from a fractured hand.
The Springboks have also had to rule out Saracens-bound loose-forward Wikus Van Heerden for the first Test following knee surgery.
South Africa's injury report will make pleasant reading for Wales, who are missing six of the side that won the Grand Slam in March.
Wales face the world champions in Bloemfontein on June 7 and Pretoria a week later without leading scrum-halves Mike Phillips and Dwayne Peel, plus full-back Lee Byrne, centre Gavin Henson, flanker Martyn Williams and hooker Huw Bennett.
The Springboks have called Bolla Conradie into their 41-man training squad following injuries to du Preez and Bulls scrum-half Heini Adams, though he could return from a bone bruise in time for the second Test.
Both Bulls full-back Zane Kirchner and dynamic Cheetahs loose forward Duanne Vermeulen will be unavailable for the Wales Tests.
New Springboks head coach Pieter de Villiers will confirm his final final squad of 30 for the Tests on Wednesday.
South Africa will include Europe-based stars John Smit and Percy Montgomery, who have been released for the Tests by Clermont Auvergne and Perpignan, plus Bath fly-half Butch James.