Such a designation is rare under global law, but has been used in contexts including Bosnia, Sudan and an Islamic State campaign against the Yazidi communities in Iraq and Syria.
Addressing the Human Rights Council on Tuesday, Zeid said United Nations investigators have received "concordant reports of acts of appalling barbarity committed against the Rohingya" during a military crackdown in Rakhine state in August.
Myanmar's ambassador to the rights council, Htin Lynn, denied atrocities had taken place and said his government and Bangladesh were working to ensure the return of displaced people.
Zeid al-Hussein had previously described the campaign by Myanmar's military as "textbook" ethnic cleansing.
The comments are among the first by United Nations officials about a possible genocide perpetrated against the Rohingya, a Muslim minority in Myanmar, more than 600,000 of whom have fled into neighboring Bangladesh since a bloody security crackdown began in August.
"Can anyone -can anyone- rule out that elements of genocide may be present?"
Speaking in September, Bangladeshi Foreign Minister Abul Hasan Mahmood Ali, around 3,000 Rohingya have been killed in the crackdown.
Officials at the United Nations have said they can not rule out the possibility of genocide being conducted against Rohingya Muslims in Myanmar by government soldiers.
Marzuki Darusman, who heads the independent fact-finding mission, told the Human Rights Council by videoconference that his team has "not yet come to any conclusion on these issues". During the visit, he will inspect the condition of Rohingya refugees living in Cox's Bazar.
Crimes included "rape, gang rape by multiple soldiers, forced public nudity and humiliation, and sexual slavery in military captivity", Patten said.
The U.N.'s top human rights body has overwhelmingly passed a measure saying that crimes against humanity have "very likely" been committed against the Rohingya minority in Myanmar.