"Although much has been done to transform the country, the national team's rugby selection criteria are racially exclusionary and biased in favour of whites," he added.
"Fikile Mbalula [the sports minister] has failed to transform rugby and any argument SARU presents to justify is failure to do so should be treated with disdain. It has betrayed the trust of millions of South Africans, continues to resist change and should attract the severest sanctions possible."
The action, which calls for the authorities responsible for the ports of exit to bar the Springboks from leaving the country, will be heard by Judge Ntendeya Mavundla.
South Africa open their World Cup campaign against against Japan on September 19. Samoa, Scotland and the United States are the other Pool C countries.
Squad:
Forwards: Willem Alberts, Schalk Brits, Schalk Burger, Lood de Jager, Bismarck du Plessis, Jannie du Plessis, Pieter-Steph du Toit, Eben Etzebeth, Siya Kolisi, Francois Louw, Frans Malherbe, Victor Matfield, Tendai Mtawarira, Trevor Nyakane, Coenie Oosthuizen, Adriaan Strauss, Duane Vermeulen.
Backs: Jean de Villiers (captain), Damian De Allende, Fourie du Preez, Bryan Habana, Zane Kirchner, Jesse Kriel, Patrick Lambie, Willie le Roux, Lwazi Mvovo, Rudy Paige, Ruan Pienaar, JP Pietersen, Handre Pollard, Morne Steyn.