Former Cosatu general secretary Zwelinzima Vavi and EFF leader Julius Malema are plotting to overthr.
One of those arrested on Sunday was the president of Turkish champions Fenerbahce, Aziz Yildirim, but the club from Istanbul has denied allegations it could have been involved in match-rigging.
"Shock" was the one-word headline in the football newspaper Fanatik.Posta wrote: "A shadow has fallen over the championship", while Milliyet wrote: "Match-fixing earthquake in football," next to a photograph of Yildirim being led away by police.
The investigation has also affected other clubs, including Besiktas and Trabzonspor. The probe is also looking at the decisive league game last season in which Fenerbahce clinched their 18th title by defeating Sivasspor 4-3.
Reports say those arrested include Sivasspor goalkeeper Korcan Celikay.