The day-old boy was stolen during visiting hours when his mother, Jasmine Naik (28), was taking an evening walk in the corridor of the hospital, they said.
She had left the baby unattended in the ward and was taking a stroll when someone took him away, police said, adding the hospital, run by a private trust, didn't have CCTV cameras.
Police said they have registered a case of kidnapping against unnamed persons.
According to eyewitnesses, they saw a saree-clad woman, aged around 25, leaving the room with the child.
Police are preparing a sketch of the suspect based on details given by the eyewitnesses.