An Indian couple had claimed they paid 120,000 rupees ($1,760) to Anima Indwar, who worked at the shelter run by the Missionaries of Charity, said police officer Aman Kumar.
Kumar said the police were investigating three other complaints against Indwar for allegedly selling children from the shelter. One more charity worker was under police questioning.
Kumar also said the police have shifted 12 pregnant women from the charity to a government-run home for care. The move apparently was to avoid any similar situation after their babies are born.
The arrests Tuesday and Wednesday followed the couple's complaint the charity worker had taken back the baby boy and kept their money.
Spokeswoman Sunita Kumar said the Missionaries of Charity was investigating.
"There was no question of selling any child as the Missionaries of Charity had stopped giving children for adoption three years ago," she said. She said the charity had never taken money from parents while arranging adoptions in the past.
Police officer Kumar said 100,000 rupees ($1,470) was recovered from the two who were arrested.
Kumar said the boy was born May 1 to a resident of the shelter and was handed to the Indian couple by Indwar on May 14 in Ranchi, the capital of Jharkhand state.
The couple told police that Indwar called them on July 1 and asked them to visit the shelter with the baby to complete some formalities.
Rupa Verma, chairperson of an organization run by the state government for children's welfare, said Indwar took the child away when the couple arrived.
The state-run organization later took custody of the boy, the Press Trust of India news agency quoted Verma as saying.
Mother Teresa started the Missionaries of Charity order in Kolkata in 1950 and it later set up hundreds of shelters that care for some of the world's neediest, people she described as "the poorest of the poor."
She received the Nobel Peace Prize for her charitable work in 1979 and Pope Francis declared her a saint last year, two decades after her death.