If passed, anyone found guilty of proselytising could face up to a year in prison.
Myanmar, a predominantly Buddhist nation of 60 million, has been grappling with sectarian violence in the western state of Rakhine since it began its transition to a half-century of military rule to democracy just three years ago.
Up to 280 people have been killed, and another 140,000 left homeless, most of them Muslims attacked by extremist Buddhists.
But because it was proposed by the Organization for the Protection of Race and Religion led by nationalist Buddhist monks accused of inflaming tensions, it is widely interpreted at being aimed at preventing Muslims from trying to coerce Buddhist women into abandoning their faith, for marriage or otherwise.
The bill would require anyone seeking to change their faith to get permission from the Religious Conversion Registration body, which is comprised of local religious and immigration officials, a local administrator, women's affairs chairman and a local education officer.
"Having to get permission from authorities for religious conversion restricts freedom of choice," she said. "Any grown-up person has the right to convert to any religion of their choice without administrative interference."
The Organisation for the Protection of Race, Religion and Belief a coalition of monks and lay people last year collected 1.3 million signatures in support of a religious conversion law.
The government sees it as politically sensitive and is now trying to measure the level of public support.