The move came as Buddhists in an unrest-hit western state vowed to boycott the census over fears it could lead to official recognition for the Rohingya, viewed by the United Nations as among the world's most persecuted minorities.
"If a household wants to identify themselves as 'Rohingya', we will not register it," government spokesman Ye Htut told reporters in Yangon.
He said people could call themselves "Bengali", a term used by the authorities who view most Rohingya as illegal immigrants from neighbouring Bangladesh.
An 11-year-old girl was killed by a stray bullet after police fired warning shots to disperse angry crowds in the state capital Sittwe.
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Humanitarian workers in the region have come under increasing pressure from Buddhist nationalists who accuse them of bias in favour of local Muslims.
The United Nations is pulling some 50 international and Myanmar staff from the region, while other major humanitarian groups are also removing their workers temporarily.
Households across Sittwe were seen Saturday bearing signs declaring: "This house is protesting against the census. Do not register".
The population tally has come under fire for its inclusion of ethnic and religious questions, which critics say will further fan the flames of unrest and threaten fragile peace talks with minority rebel groups.
UNFPA declined to comment directly on the move to ban Rohingya being registered but said in a statement that people "must feel safe to answer all questions freely".