The ban, which came into effect over the weekend in Tamil Nadu, on India's southern tip, was hailed by many in the Hindu majority on Monday.
They accuse missionaries from other religions of converting poor Hindus through offers of money and jobs or through coercion.
Some also claim that members of Hinduism's lowest untouchable caste might be induced to change faiths with hopes of losing their social stigma and opening the doors to better paid jobs and education.
Leaders from the minority Christian and Muslim communities deny such claims and say the ban violates religious freedoms guaranteed by India's constitution.
The new law carries a maximum fine of three years in prison for those found converting people against their will or through various forms of inducement. The ban was brought in by the state government and is immediately enforceable, but must be ratified by the state assembly at its next session to stay in effect permanently, officials said.
The debate over the rights and wrongs of religious conversions can be explosive in India, even though the nation of more than 1 billion people is, at least on paper, secular.
In February, a Muslim mob burned a train carrying Hindu pilgrims, triggering a wave of sectarian clashes that killed more than 1,000 people - mostly Muslims - in western Gujarat state.
Hindus make up about 81 percent of the population, Muslims constitute nearly 14 percent and Christians 2 percent, with the rest following other faiths, like Buddhism.
``Forcible or induced conversion is an oxymoron. It is not possible, and is rejected by the church,'' the All India Christian Council said in a statement Monday.
Thousands of Hindus have also converted in the past to Buddhism and Islam. Hindu nationalists have tried to convert some of them back, but Hinduism does not seek converts, as Christianity and Islam do.
Hindu villagers allegedly burned alive Australian Christian missionary Graham Stewart Staines and his two sons in the eastern Indian state of Orissa in 1999 after they accused him of carrying out conversions.
The Orissa state government has a law similar to the one adopted in Tamil Nadu, and requires would-be converts to first secure permission to change faiths from local authorities.
Christian organizations also argue that the Orissa law violates guarantees of religious freedom enshrined in India's constitution.
The All India Christian Council said it would launch a court challenge to the Tamil Nadu ban even though similar legal action has proved time-consuming, costly and so far unsuccessful in Orissa.
A Muslim political party in Tamil Nadu said the Tamil Nadu law was vague and open to misuse by officials.
``Terms like 'allurement' and `coercion' used in the law have such a loose definition that they provide ample opportunity for anyone to use them to browbeat the minority,'' said A.S. Jawahirullah, a leader of the Tamil Nadu Muslim Munnethra Kazhagam.
In contrast, one of Indian Hinduism's senior holy men, Jayendra Saraswathi, said a ban on conversions should be enacted nationally.
``It is a pity that even after 50 years of independence, conversions are taking place in the name of God,'' he said.
A former Supreme Court judge, V. Ramaswamy, now a member of Tamil Nadu's ruling party, said the law did not violate religious freedoms.
``On the contrary, it only goes to strengthen that right by ensuring that the individual is not forced or lured into practicing some other religion instead of his own,'' he told The Associated Press.