Police busted the illegal adoption racket after they found three newborns inside a cardboard box being taken from a clinic north of Kolkata on Monday night.
The clinic owner and seven others were arrested on Monday, and four others were detained Wednesday after raids on other clinics.
One of the stolen babies, a girl, has been reunited with her parents, while the mothers of the other two were still being identified, senior police officer Bharatlal Meena told AFP.
All the babies were between three and five days old, he said.
"We fear that at least 45 newborns were trafficked by the gang over the past two years," Meena said, adding the clinics were paid 200,000 rupees ($2,900) for a boy and half that for a girl.
"Some of the women admitted to the nursing home (clinic) were told that they have given birth to stillborn babies," he said.
"If a mother wanted to see her baby, the nursing home employees would tell her that that it would be a scary sight. Most of the time parents would return home without seeing their babies."
The babies were stolen from at least four clinics in the area and were kept in boxes before being handed over to a charity.
The charity passed the babies to an agent who worked for prospective adoptive parents, Meena said.
"Investigators have obtained evidence that babies born in this nursing home had been trafficked to several cities, including one in the US."
Last year, police in New Delhi busted a charity that had allegedly sold two dozen babies and toddlers to couples for up to 550,000 rupees each.
Kidnapping and trafficking children in India has long been a major problem, with many sold to unscrupulous employers for use as cheap labour.
The racket in Delhi involved prospective adoptive mothers being admitted to private clinics where they were given a false record of having delivered a baby as well as a birth certificate for their "newborns".
Experts say couples wanting to legally adopt in India are often frustrated by lengthy bureaucratic delays and complex rules, pushing them towards the thriving illegal adoption market.
Desperately poor parents also sometimes sell their children, while others are kidnapped by traffickers, experts say.
India has an estimated 30 million orphans. But only 4,362 children were legally adopted in 2014 and 3,677 in 2015, according to the government's central adoption authority.