CCTV footage showed a group of men smashing plant pots, breaking down doors and shattering windows in the grounds of the cathedral in Madhya Pradesh state late Friday.
The right-wing Hindu Dharma Sena group had accused the church of converting around 200 people from local tribal groups to Christianity, although it denies causing any damage to church property.
“We arrested six men last night in connection with the vandalism. We are trying to identify more people… there may be more arrests,” HC Mishra, a senior state police official, told AFP by telephone.
Religious conversions are highly controversial in India, a secular country where religious freedom is considered a fundamental right.
Critics say Hindu hardline groups have become emboldened since the Hindu nationalist Bharatiya Janata Party (BJP) won power in India last year.
The latest attack comes at a time of heightened sensitivity over religious freedom in India, where churches and a Christian school have been attacked in recent months.
Masked men on Saturday attacked a church in Mumbai, capital of western Maharashtra state, which like Madhya Pradesh is ruled by the BJP.
Earlier this month, an elderly nun was raped at a convent school in the eastern state of West Bengal, triggering protests across the country.
India’s Prime Minister Narendra Modi last month pledged to crack down on religious violence and ensure freedom of worship for all faiths.
He had been criticised for not speaking out earlier.
India is 80 percent Hindu while Muslims make up 13.4 percent of the 1.2 billion population. Christians, Buddhists, Sikhs and other religions account for the rest. – AFP