Other policies detailed by Fortify Rights, based in Southeast Asia, include restrictions on movement and marriage by the Rohingya who live mainly in Myanmar's northeastern Rakhine State.
The group says its 79-page report, released Tuesday, is based "primarily on the analysis of 12 leaked official documents and a review of public records, as well as interviews with Rohingya and others in Myanmar and Thailand."
The report, "Policies of Persecution: Ending Abusive State Policies Against Rohingya Muslims in Myanmar," says "Regional Order 1/2005," obtained by Fortify Rights, lays the foundation for a two-child policy enforced in Maungdaw and Buthidaung townships.
The order states Rohingya "who have permission to marry" must "limit the number of children, in order to control the birth rate so that there is enough food and shelter."
Fortify Rights said the order "translates to a strict two-child policy" and "prohibits Rohingya from having children out of wedlock."
The report also claims Rohingya in Rakhine must have official permission to travel between townships or out of the state.
"The government is systematically persecuting Rohingya on the basis of ethnicity, religion and, at times, gender," said Matthew Smith, director and founder of Fortify Rights.
"Rohingya women, in particular, find themselves in the cross-hairs of these targeted policies, facing severe discrimination because they're women as well as Rohingya Muslims."
Smith said there should be an independent investigation by international groups and other groups within Myanmar into human rights abuses against Rohingya.
The treatment of Myanmar's estimated 800,000 Rohingya has been an international focus as the mostly Buddhist country struggles to evolve from decades of military dictatorship into a democracy.
Rohingya Muslims, who speak a language related to Bengali, live mostly in Rakhine on the border with Bangladesh.
The United Nations has said about 140,000 have been forced out of their homes in Rakhine and live as internal refugees, while others have fled to Bangladesh either across the border or by boat.
Anti-Muslim violence has spread to other provinces. In March last year, 43 Muslims were killed in Meiktila in the Mandalay region, while a mosque and a boarding school were burned in Lashio in Shan state the previous month.
The Office of the U.N. High Commissioner for Human Rights last month called for an "impartial investigation" into reports of mass killings of Rohingya in Rakhine.
The agency in a news release said it had received "credible information" eight Rohingya Muslim men were attacked and killed Jan. 9 in Du Chee Yar Tan. It said four days later during a clash in the same village a police sergeant was captured and killed by the Rohingya villagers.
Later the same evening, at least 40 Rohingya Muslim men, women and children were killed by police and civilians.
U.S. State Department spokeswoman Jen Psaki said last month the government was "saddened" over reports of the deaths and violence.
Myanmar's opposition leader and Nobel Peace Prize laureate Aung San Suu Kyi has spoken out against the violence.
She told the BBC in October that violence between Buddhists and Muslims in the country shows a "climate of fear" has gripped both groups, but "it's not ethnic cleansing."