This after Accountability Now lodged a complaint with the council after several court judgments against Mkhwebane.
The council confirmed that they had referred the complaint against the public protector to a relevant structure.
Chairperson of the council Hlaleleni Dlephu said they met a week ago to discuss the matter.
“The complaint was sent to the relevant provincial office for processing, like all other complaints received by the council,” said Dlephu.
“While the complaint is being processed, the LPC is prohibited by the Legal Practice Act from discussing the matter,” she added.
This week, the North Gauteng High Court will make a ruling on the case between President Cyril Ramaphosa and Mkhwebane on the matter of Minister of Public Enterprises Pravin Gordhan.
In her report, Mkhwebane had ordered Ramaphosa to take disciplinary action against Gordhan over the granting of an early pension to former Sars Deputy Commissioner Ivan Pillay. But Ramaphosa has said he would not be able to take action because there is a judicial review by Gordhan.
Ramaphosa has taken Mkhwebane to court again over her findings against him on the Bosasa donation into his presidential campaign.
In the complaint to the LPC, Accountability Now said Mkhwebane needed to be investigated and struck off the roll of advocates for her conduct.
Recently, the Constitutional Court ruled in favour of former senior prosecutors Nomgcobo Jiba and Lawrence Mrwebi after they were struck off the roll of advocates.
The General Council of the Bar had successfully applied in the high court that they be struck off the roll.
The Supreme Court of Appeal upheld the high court decision. However, the Constitutional Court overturned it.
Mkhwebane now faces an investigation by the LPC.
However, the council would not say how soon it would conclude its investigation and take a decision.
It said it would not comment on the issue until there was a decision. Mkhwebane was slapped with a personal cost order by the Constitutional Court on the Sars matter.
She had ordered Parliament and the Justice Committee to amend the Constitution and change the mandate of the bank.
This raised the ire of the national legislature and the court ruled against her.
The Justice Committee is meeting in September to discuss the request by the official opposition for the removal of the public protector.
The DA has in the past two attempts failed to get Mkhwebane removed from her position.
But civil society and some in the tripartite alliance want her to be removed.