Malema took aim at Gordhan last November, accusing him of removing black officials from state-owned enterprises.
Gordhan had wanted Malema to donate R150 000 to charity, apologise and pay costs.
“Despite the fact that the utterances were indeed hateful and aimed at engendering hatred against the applicant, the applicant has failed to bring his understandable grievance within the compass of the Equality Act,” Judge Roland Sutherland ruled on Thursday.
This is the second case involving hate speech that the EFF has won at the Equality Court.
Two weeks ago, the court ruled against the South African National Editors Forum (Sanef) which had brought a case accusing Malema and his party members of harassing journalists on social media platforms.