Bishop John Thattungal, 58, will be barred from performing any religious or administrative duties until a formal inquiry into his conduct is completed, said the Rev. Stephen Alathara, a spokesman for the Kerala Catholic Bishops' Council, in a telephone interview from the southern Indian city of Kochi.
Alathara said the bishop's adoption of the woman earlier this year had upset other priests in the Kochi diocese.
"The majority of the priests were unhappy and asked for his resignation," he said, adding that the Vatican ordered the suspension on Thursday.
He said there are questions surrounding the legality of the adoption because the woman is not a minor.
Thattungal could not be reached for comment, but news reports in Kerala have quoted him as saying, "I have only fatherly love toward the woman who has spiritual powers. This relation is giving me spiritual refreshment."
A three-member committee of bishops will investigate Thattungal's conduct and submit a report to Archbishop Daniel Acharuparambil, the president of the Kerala Catholic Bishops' Council, who will then forward it to the Vatican, Alathara said.
The investigating committee does not have a set deadline, but the Vatican has asked for a report "as early as possible," he said.
Christians make up 2.5 percent of India's 1.1 billion people, the majority of whom are Hindus.