The suspension stems from the red card he received during Bafana Bafana's opening match of the tournament against co-hosts Mexico.
“We are disappointed with the outcome of our appeal because we strongly believe that the punishment is far harsher than the offense that Themba is said to have committed,” SAFA said in a statement.
As a result, the experienced midfielder will miss South Africa's knockout tie against fellow co-hosts Canada in Los Angeles on June 28, serving the final game of his ban.
There was, however, some positive news for Bafana Bafana, with midfielder Teboho Mokoena available for selection again after completing a one-match suspension.
His return provides a timely boost for South Africa as they prepare for a crucial World Cup encounter against hosts Canada.