Chief Justice David Maraga said the demonstrations were "clearly intended to intimidate individual judges".
Maraga and his fellow judges are putting the final touches to their highly-anticipated full judgement, expected to be read out Wednesday, which will point out in detail why they took the unprecedented decision to overturn the August 8 poll.
Maraga in his brief ruling nearly three weeks ago mentioned only "irregularities and illegalities" in the transmission of vote results, when he annulled Kenyatta's victory over his rival Raila Odinga.
While the chief justice became an overnight hero to many across the continent, he inspired fury among the ruling party.
Kenyatta took to the streets referring to Maraga and his fellow judges as "crooks", and threatened to "fix" the Supreme Court if re-elected.
He then attempted to row back on his comments, saying he was merely angry, in what was seen as attempt to appease Maraga's Kisii community -- an important voting bloc -- ahead of the new election.
However local media has reported moves by ruling party lawmakers to curb the powers of the Supreme Court.
Maraga said: "Individual judges particularly of the Supreme Court as well as other judicial officers and staff have been attacked, threatened and negatively profiled on social media.
"Senior political leaders have also threatened the judiciary promising to cut it to size and teach us a lesson."
He said the police had ignored calls to act on these threats.
Maraga, who was speaking on behalf of the Judicial Service Commission, said such "attacks are degrading, demeaning and are meant to intimidate, threaten and cow the institution and cow the judges".
"If leaders are tired of having a strong and independent judiciary they should call a referendum and abolish it all together," he added.
"Before that happens, the judiciary will continue to discharge its mandate in accordance to the constitution."
According to Maraga's ruling Kenya must hold a new election by October 31.
The embattled electoral commission set the new poll for October 17, a date looking less and less likely as the main players bicker over how to hold a credible poll.
The French firm providing technology for identifying voters and transmitting results said Monday its system would not be ready in time.