Police took action after the state's Child Welfare Committee (CWC) registered a complaint.
"What these people did - for around 100,000 to 120,000 rupees, they sold the baby to a couple when the baby was less than a month old, sometimes straight from the hospital", he said.
Police officer Aman Kumar told Thomson Reuters Foundation, "They have said that at least five to six babies have been sold to childless couples".
In regards to Mother Teresa's charity, authorities are taking a closer to see how many children and families have been affected.
"If this was a lucrative trade, there is reason to believe other centres operated by MoC or other shelter homes also may be indulging in such activities", senior police officer RK Mallick told NDTV.
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One nun and another staff member were reportedly arrested on the grounds at the Mission of Charity in Jharkhand for allegedly selling a baby to an Indian couple for around $1,700, The Daily Mail noted.
Both Nirmal Hriday and Shishu Niketan are run by Mother Teresa-founded Missionaries of Charity.
Incidentally, in January 2014, then child welfare panel chairperson Om Prakash Singh had in a letter to the state government alleged "child trafficking" from both Jail Road and Hinoo shelters. It is completely against our moral conviction.
The baby, a boy, was born to a young woman who arrived at the charity on 19 March, and was sold to the couple on 14 May, Ms Kumari said. "When they did not find Anima around, they went to the Missionaries of Charity but were not entertained by the following which the couple approached us and the matter was disclosed", she said. "We will take all necessary precautions that it never happens again if it has happened", said MoC spokeswoman Sunita Kumar.
The CWC in the recent past has been constantly monitoring the situation at the Missionaries of Charity.
As per norms, any child or girl brought to a shelter home has to be reported to the CWC and any adoption done according to Central Adoption Resource Authority guidelines.
The Missionaries of Charity stopped giving babies up for adoption in 2015 after India changed its adoption laws.