Ramaphosa's spokeswoman, Khusela Diko, said: "We cannot dignify such rants with a response."
Malema's frontal attack on Gordhan was similar to how his deputy, Floyd Shivambu, had also taken aim at National Treasury deputy director-general Ismail Momoniat, who is known to be close to Gordhan.
Shivambu accused Momoniat of being part of an Indian cabal and "a neo-liberal technocrat who doesn't respect African leadership".
Malema said he wished to be invited to give evidence at the ongoing commission of inquiry into how SARS was used as a political weapon.
"My houses were taken by Pravin, I was humiliated by Pravin," he said.