Malema also said the current stock of judges was "traumatised old people".
The GCB said that if the comments were correctly reported, it was remarkable that these statements were made only a few days after two judgments were handed down by women in matters where the EFF was an unsuccessful party.
The GCB said it supported a statement made by Chief Justice Mogoeng Mogoeng in 2015 when he said although judges should be susceptible to constructive criticism, that criticism should be fair and in good faith.
"The GCB does not seek by means of this statement to debate the correctness or otherwise of the two judgments... or to attempt to stifle debate on that regard.
"We do, however, wish to to express our concern that instead of offering a reasoned critique of the judgment, Mr Malema launched a veiled attack of a personal nature on the individual judges who delivered those judgments, by implication referring to them as being incompetent, lacking in appropriate confidence , independence, and being politically motivated," the GCB said.
It added that as a party to the judgments in question, the EFF had the right to seek to appeal against them, which the party had publicly indicated it would do.
"But in doing so, they will be required to advance valid grounds why the judgments are legally incorrect."