The Asian country's new law retains the definition of the state as secular and says all religions will be treated the same but Christian campaigners are concerned.
Section 26 of the constitution makes it illegal to "convert another person from one religion to another".
It also criminalises "any act or behaviour to undermine or jeopardize the religion of another".
Christian Solidarity Worldwide (CSW) said it means choosing and changing one's faith will no longer be seen as a "positive individual choice".
Nepal has seen an increase in religious tension in recent years following bomb attacks on churches in the country.
CSW's Special Ambassador Stuart Windsor said: "While we welcome the recent decision of the CA to maintain state neutrality towards all religions, it is vital that the anti-conversion clauses in the new constitution do not lead to the persecution of members of minority religions who wish to explain and discuss their beliefs with people of other faiths; nor that individuals who help others without coercion to make a free choice to adopt a new faith are liable to prosecution.
"CSW is also concerned at the recent bomb attacks on churches. While the authorities must ensure that the perpetrators are brought to justice, we welcome the interfaith dialogue that has taken place as it is important for the future peace of Nepal that religious leaders meet to remedy misunderstandings and foster reconciliation between members of different faiths."