The police action came after a photograph from a CCTV footage from the hospital was published in the media.
The police arrested four persons - a couple and two women - and rescued two stolen babies from their possession.
While one baby was stolen from the SCB Hospital on Wednesday, the other one was lifted in January, police said.
Both the babies are now under treatment of the hospital and efforts were on to hand them over to their respective parents.
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Minati, who works in a private hospital in Bhubaneswar as a house keeper, used to frequent the SCB Hospital masquerading as an Accredited Social Health Activist (ASHA).
Winning the trust of the mothers, she used to take the newborns for immunisation and flee, police said.
"More arrests would be made as the investigation progresses," he said.
The arrested couple had purchased one of the two rescued babies.