Myanmar's army says it has been targeting Rohingya militants.
It is estimated that more than 600,000 Rohingya have fled to neighbouring Bangladesh to escape the violence which has been escalating since the summer. They include indiscriminate shooting and stabbing of villagers, rape, beatings and the burning of houses with families inside.
Thirty-three of the council's 47 members backed the text listing a long line of horrific abuses, including summary killings of children, rape, torture and large-scale forced displacement, which it said indicated "the very likely commission of crimes against humanity".
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, who has described the campaign in the past as a "textbook case of ethnic cleansing", was addressing a special session of the UN Human Rights Council called by Bangladesh.
However, while ethnic cleansing is not a designated offence under global law, genocide is the most serious of atrocity crimes.
"But the concerns are extremely serious, and clearly call for access to be immediately granted for further verification".
Zeid al-Hussein urged the United Nations to set up a new mechanism to allow criminal prosecutions of individuals suspected to be responsible.
Genocide is defined by the United Nations as "acts committed with the intent to destroy, in whole or in part, a national, ethnic, racial or religious group".
The UN first defined it in the Convention on the Prevention and Punishment of the Crime of Genocide in 1948.
Myanmar has not granted the investigators access to Rakhine, the northern state from which the Rohingya have fled, Darusman said. Some 100 caricatures depicting the tribulation and suffering of the ethnic Rohingya in Myanmar and the efforts of Malaysia in helping the community are on display for five days at the Putra World Trade Centre (PWTC) here until Saturday. After the latest wave of arrivals it now hosts more than a million Rohingya.