The Jubilee lawmaker wants the Judicial Service Commission, the employer of judges and magistrates, to investigate the conduct of Judge Maraga since his appointment as Chief Justice.
Mr Wambugu accuses the CJ of instituting "a judicial coup" as the head of the third arm of government.
Kenya's Chief Justice David Maraga is under siege after the Supreme Court quashed the re-election of President Kenyatta.
On Thursday, an MP from central Kenya Ngunjiri Wambugu filed a petition before the Judicial Service Commission (JSC) seeking the removal of the country's top judge.
In the 14-page petition, Mr Wambugu accuses the president of the Supreme Court of “gross misconduct”.
The ruling Jubilee party Nyeri Town MP wants JSC, the judges and magistrates' employer, to investigate the conduct of judge Maraga since his appointment as Chief Justice.
Mr Wambugu accuses the CJ of instituting "a judicial coup" as the head of the third arm of government.
He further claims judge Maraga has been held captive by a group of NGOs who have been campaigning against Mr Kenyatta's presidency since 2013.
He alleges that the CJ has allowed the non-profits to be embedded in the Judiciary and has been funding a number of programmes, including technical support and training at the Judicial Training Institute.
Judge Ibrahim
Mr Wambugu has also accused the CJ of preventing Justice Mohamed Ibrahim from participating in the hearing of the presidential petition filed by Mr Odinga.
Justice Ibrahim fell sick on the second day of the hearing of the case.
The allegations come as Kenyans eagerly await the full judgement of the Supreme Court, which nullified the August 8 re-election of President Kenyatta. The court has nine days left to issue its decision in full.
Justice Maraga, deputy Chief Justice Philomena Mwilu, Smokin Wanjala and Isaac Lenaola nullified the election citing irregularities and illegalities in the transmission of results.
