The nationality of the 45-year-old passenger is still unclear and the case was handed over to state's Wildlife Crime Bureau.
All seemed well until staff's suspicions were raised when they heard a noise from the man's bag and eventually discovered the one-month-old 1kg (2.2lbs) leopard cub.
He said they are investigating whether the man was carrying the leopard as part of an global smuggling chain. "The custom officers fed the cub milk in a feeding bottle and re-energised the cub", said the press statement.
He had been cornered by officials as he attempted to quickly leave the area after collecting his luggage.
According to a statement from the Office of the Commissioner of Customs, "It was observed that a faint trill sound was coming from his checked-in luggage".
Up until three months old, leopard cubs rely exclusively on the constant care of their mothers for milk and protection - even in captivity they receive round the clock care. The leopard cub was kept inside a pink plastic basket, said an official release.
"He says he was supposed to handover it to someone at the Chennai airport", said a senior officer.
"The Cub will be rehabilitated in the Aringar Anna Zoological Park and the forest department will take appropriate action against the passenger under wildlife protection Act 1972", said Chaudhary.