Local officials said the new measure -- part of a policy that will also ban polygamy -- will be applied to two Rakhine townships that border Bangladesh and have the highest Muslim populations in the state. The townships, Buthidaung and Maundaw, are about 95 per cent Muslim.
The measure was enacted a week ago after a government-appointed commission investigating the violence issued proposals to ease tensions, which included family planning programs to stem population growth among minority Muslims, said Rakhine state spokesman Win Myaing.
"The population growth of Rohingya Muslims is 10 times higher than that of the Rakhine (Buddhists)," Win Myaing said.
"Overpopulation is one of the causes of tension."
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Sectarian violence in Myanmar first flared nearly a year ago in Rakhine state between the region's Rakhine Buddhists and Muslim Rohingya.
Mobs of Buddhists armed with machetes razed thousands of Muslim homes, leaving hundreds of people dead and forcing 125,000 to flee, mostly Muslims.
Since the violence, religious unrest has morphed into a campaign against the country's Muslim communities in other regions.
Win Myaing said authorities had not yet determined how the measures will be enforced, but the two-child policy will be mandatory in Buthidaung and Maundaw. The policy will not apply yet to other parts of Rakhine state, which have smaller Muslim populations.
Predominantly Buddhist Myanmar does not include the Rohingya as one of its 135 recognised ethnicities. It considers them to be illegal immigrants from Bangladesh and denies them citizenship. Bangladesh says the Rohingya have been living in Myanmar for centuries and should be recognised there as citizens.
Muslims account for about 4 per cent of Myanmar's roughly 60 million people.