The Ministry of Women, Children and Social Welfare said it imposed the ban as part of a package of measures after rescuing more than 50 children.
"We fear that traffickers might try to cash in on the situation people are in right now, and have taken these decisions to protect vulnerable children," said ministry spokesman Ram Prasad Bhattarai.
Impoverished Nepal's porous border with India made it a prime target for traffickers even before last month's quake, which campaigners say has worsened the problem.
The government has also made it mandatory for children travelling without their parents to carry a permission letter from local authorities.
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"We are on high alert 24 hours and are strictly checking papers at border areas before allowing any crossings," said police spokesman Kamal Singh Bam.
A cycle of unemployment and poverty and the impact of a 10-year Maoist insurgency has made Nepali women and children easy targets for traffickers.
Several countries, including the US and Canada, suspended adoptions from Nepal in 2010 after discovering some private orphanages were faking documents to make it appear that children whose parents were still living had been orphaned.
"There is a threat that these children will be used for child labour, be sexually exploited or even be sold to sex trade," he added.
More than 8,600 people died in two major quakes that hit Nepal on April 25 and May 12, destroying nearly half a million houses and leaving thousands desperate for food, shelter and water.
Thousands more have been left homeless and are camping out in the open, with just weeks to go until the monsoon rains.