This shocking photo clearly shows their young son inside a bag, going through an X-ray machine.
The couple were arrested as they arrived at the airport from Egypt on Saturday morning, Gulf News reports.
Hand luggage is usually scanned at Emirati airports on arrival, after passengers have had their passports stamped.
It is reported that the little boy didn't have a visa, passport or official documents.
"When customs officials saw the baby inside the bag at the X-ray scanner, they were stunned," a police officer told Gulf News.
"This machine is very dangerous for anyone, let alone a baby in a bag to pass through. A case will now be raised against the mother and father, they both have visas to come to the UAE, but they have put the life of their child at risk."
The little boy is being cared for by the authorities, according to reports.