District magistrate Pritha Sarkar ordered the inquiry after her attention was drawn by scribes into the alleged incident at Jalpaiguri state general hospital here.
She said NGO Childline would investigate the incident and take necessary steps.
A beggar woman from the neighbourhood of Denguaghat tea estate had allegedly sold her new-born male child for Rs 13000 in the hospital. She has three daughters.
Denying any sale of new-born from the hspital, its superintendent Sushanta Ray said the 35-year-old woman named Gouri Das had been admitted to the hospital on May 25 and delivered a male child weighing 3.1 kg the next day.
A person named Bapi Saha Roy had accompanied the couple, he said adding "We do not know whether the infant was sold."
Police said no complaints had been filed.