The EFF wants deputy president Paul Mashatile to account under oath for his dealings with the consortium to whom the lucrative licence to operate the national lottery was awarded.
The licence is said to be to the value of more than R80bn.
The EFF challenge is effectively an attempt to redefine what constitutes direct interest, with the party arguing the grey area in the wording of the national lottery tender opened the door for politicians to abuse the process through family members.