Manila hit back at "irresponsible and disrespectful" commentary by the UN official.
Mr Zeid's comments on Friday come amid deteriorating relations between Manila and the UN, and followed the government's decision to include a UN special rapporteur on a list of 600 people they want to class as "terrorists".
The woman in question - Vicky Tauli-Corpuz says she now fears for her safety.
"We are shocked that the Special Rapporteur is being targeted because of her work defending the rights of indigenous peoples", said Michel Forst, the Special Rapporteur on the situation of human rights defenders, and Catalina Devandas Aguilar, Chairperson of the Coordination Committee of the Special Procedures.
"As an agency of the UN, the Office of the United Nations High Commissioner for Human Rights is expected to fulfill its duties within the framework set out by the purposes and principles of the UN Charter".
Her fellow UN rapporteurs also joined Tauli-Corpuz in denouncing her inclusion, saying this was in retaliation of her statements condemning violations against the lumad communities, particularly in Mindanao.
He said the Philippine leader "needs to submit himself to some sort of psychiatric examination".
"So all officials of the United Nations must in fact discharge their functions towards realizing the avowed goals of the UN system and should not resort to abusing and disrespecting elected heads of states of UN member states".
Critics said Duterte in his public pronouncements ordered or encouraged policemen to kill those involved in drug trafficking, resulting in thousands of alleged extrajudicial killings.
The petition said the rebels were "using acts of terror" to sow fear and panic to overthrow the Government.
United Nations High Commissioner for Human Rights Zeid Ra'ad Al Hussein speaks in Guatemala City on November 17, 2017.
Sison, who is also the NDFP chief political consultant, on Thursday said President Rodrigo Duterte was "engaged in a wild anti-communist witch-hunt under the guise of anti-terrorism".
"I don't think he's in a position to do it (throw UN envoys to crocodiles)".
Cayetano said the Philippines was bothered by "the manner in which a ranking UN human rights official can overstep his mandate". "There will be no occasion to push them to crocodiles", Presidential Spokesperson Harry Roque Jr. said in a press conference.
Sison dismissed the terrorism charges as baseless, as he underscored that he had already won legal cases for the removal of his name from the European Union (EU) list of terrorists, as well as the dismissal of murder charges fabricated against him by the Arroyo regime.