Zeid said some about 626,000 Rohingya have fled since August, and many more are continuing to pour into Bangladesh.
The United Nations human rights chief, Zeid Ra'ad al-Hussein, said in Geneva on Tuesday that Burmese security forces may be guilty of genocide, adding worldwide pressure on Myanmar to be investigated for crimes against humanity.
Mainly Buddhist Myanmar denies the Muslim Rohingya are its citizens and considers them foreigners.
Myanmar's ambassador in Geneva, Htin Lynn, denied any state efforts at "dehumanization" of the Rohingya, saying it "could be an act of extremist individuals".
These included allegations of security forces "deliberately burning people to death inside their homes; murders of children and adults; indiscriminate shooting of fleeing civilians; widespread rapes of women and girls; and the burning and destruction of houses, schools, markets and mosques", he added.
The measure broke little new ground but did instruct the United Nations human rights office to assess the level of cooperation of Myanmar's government with United Nations rights monitors and other experts.
China, the Philippines and Burundi voted against the measure. Two delegations in the 47-member council were not present.
These four fearless Rohingya Muslims have told their chilling stories after escaping Myanmar and reaching Bangladesh.
Marzuki Darusman, head of an independent global fact-finding mission on Myanmar, said by video from Malaysia: "We will go where the evidence leads us". Myanmar's army says it has been targeting Rohingya militants.
He spoke at a special council session on the Rohingya on Tuesday.
In the sprawling camps of southern Bangladesh, now home to over 800,000 Rohingya, many say they would prefer to remain there, because they do not trust Myanmar's assurances of safe return.
Zeid, however, said no repatriation of Rohingya to Myanmar should occur without "sustained human rights monitoring" to ensure they can live safely.
The council's resolution broke little new ground other than calling for Zeid's office to report on Myanmar's cooperation with United Nations rights investigators.