Not only that, the party has also expressed willingness to take the matter to the "highest court" and embarrass Speaker Baleka Mbete.
Shivambu is the first MP to be referred to the newly-constituted disciplinary committee, for comments made in 2016 when he told the ruling party that President Jacob Zuma was going to kill them.
"As the EFF, we unequivocally reject the Speaker's move as deliberate suppression of free speech in Parliament," EFF spokesperson Mbuyiseni Ndlozi said.
He cited the powers, privileges and immunities act, and the Constitution, on the free speech enjoyed by MPs.
'Biased, only protects Zuma'
Ndlozi said the Speaker violated the powers and privileges act by referring Shivambu to the committee for what he said during a debate.
The referral sought to create fear on parliamentary debates on Zuma, the EFF said.
"The EFF is willing to go to the highest court in the land to defend free speech in Parliament.
"We demonstrated this when we won the court case regarding CIC Julius Malema's remarks that 'the ANC government killed workers in Marikana'. We will also embarrass Mbete and her partisan rulings in relation to our [EFF's] deputy president's recent remarks," Ndlozi said.
The EFF spokesperson said the party had repeatedly written to the Speaker asking her to refer Zuma to a disciplinary committee and to initiate impeachment proceedings against him, without success.
"She is biased and only protects Zuma. This is why the EFF has been calling for her removal from the beginning of the fifth democratic Parliament. Her decision to charge the DP of EFF is legally invalid and it is tainted with bias based improper political motives."